rfc9340.original | rfc9340.txt | |||
---|---|---|---|---|
Quantum Internet Research Group W. Kozlowski | Internet Research Task Force (IRTF) W. Kozlowski | |||
Internet-Draft S. Wehner | Request for Comments: 9340 S. Wehner | |||
Intended status: Informational QuTech | Category: Informational QuTech | |||
Expires: 1 March 2023 R. Van Meter | ISSN: 2070-1721 R. Van Meter | |||
Keio University | Keio University | |||
B. Rijsman | B. Rijsman | |||
Individual | Individual | |||
A. S. Cacciapuoti | A. S. Cacciapuoti | |||
M. Caleffi | M. Caleffi | |||
University of Naples Federico II | University of Naples Federico II | |||
S. Nagayama | S. Nagayama | |||
Mercari, Inc. | Mercari, Inc. | |||
28 August 2022 | February 2023 | |||
Architectural Principles for a Quantum Internet | Architectural Principles for a Quantum Internet | |||
draft-irtf-qirg-principles-11 | ||||
Abstract | Abstract | |||
The vision of a quantum internet is to enhance existing Internet | The vision of a quantum internet is to enhance existing Internet | |||
technology by enabling quantum communication between any two points | technology by enabling quantum communication between any two points | |||
on Earth. To achieve this goal, a quantum network stack should be | on Earth. To achieve this goal, a quantum network stack should be | |||
built from the ground up to account for the fundamentally new | built from the ground up to account for the fundamentally new | |||
properties of quantum entanglement. The first quantum entanglement | properties of quantum entanglement. The first quantum entanglement | |||
networks have been realised [Pompili21.1], but there is no practical | networks have been realised, but there is no practical proposal for | |||
proposal for how to organise, utilise, and manage such networks. In | how to organise, utilise, and manage such networks. In this | |||
this draft, we attempt to lay down the framework and introduce some | document, we attempt to lay down the framework and introduce some | |||
basic architectural principles for a quantum internet. This is | basic architectural principles for a quantum internet. This is | |||
intended for general guidance and general interest, but also to | intended for general guidance and general interest. It is also | |||
provide a foundation for discussion between physicists and network | intended to provide a foundation for discussion between physicists | |||
specialists. This document is a product of the Quantum Internet | and network specialists. This document is a product of the Quantum | |||
Research Group (QIRG). | Internet Research Group (QIRG). | |||
Status of This Memo | Status of This Memo | |||
This Internet-Draft is submitted in full conformance with the | This document is not an Internet Standards Track specification; it is | |||
provisions of BCP 78 and BCP 79. | published for informational purposes. | |||
Internet-Drafts are working documents of the Internet Engineering | This document is a product of the Internet Research Task Force | |||
Task Force (IETF). Note that other groups may also distribute | (IRTF). The IRTF publishes the results of Internet-related research | |||
working documents as Internet-Drafts. The list of current Internet- | and development activities. These results might not be suitable for | |||
Drafts is at https://datatracker.ietf.org/drafts/current/. | deployment. This RFC represents the consensus of the Quantum | |||
Internet Research Group of the Internet Research Task Force (IRTF). | ||||
Documents approved for publication by the IRSG are not candidates for | ||||
any level of Internet Standard; see Section 2 of RFC 7841. | ||||
Internet-Drafts are draft documents valid for a maximum of six months | Information about the current status of this document, any errata, | |||
and may be updated, replaced, or obsoleted by other documents at any | and how to provide feedback on it may be obtained at | |||
time. It is inappropriate to use Internet-Drafts as reference | https://www.rfc-editor.org/info/rfc9340. | |||
material or to cite them other than as "work in progress." | ||||
This Internet-Draft will expire on 1 March 2023. | ||||
Copyright Notice | Copyright Notice | |||
Copyright (c) 2022 IETF Trust and the persons identified as the | Copyright (c) 2023 IETF Trust and the persons identified as the | |||
document authors. All rights reserved. | document authors. All rights reserved. | |||
This document is subject to BCP 78 and the IETF Trust's Legal | This document is subject to BCP 78 and the IETF Trust's Legal | |||
Provisions Relating to IETF Documents (https://trustee.ietf.org/ | Provisions Relating to IETF Documents | |||
license-info) in effect on the date of publication of this document. | (https://trustee.ietf.org/license-info) in effect on the date of | |||
Please review these documents carefully, as they describe your rights | publication of this document. Please review these documents | |||
and restrictions with respect to this document. Code Components | carefully, as they describe your rights and restrictions with respect | |||
extracted from this document must include Revised BSD License text as | to this document. | |||
described in Section 4.e of the Trust Legal Provisions and are | ||||
provided without warranty as described in the Revised BSD License. | ||||
Table of Contents | Table of Contents | |||
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 | 1. Introduction | |||
2. Quantum information . . . . . . . . . . . . . . . . . . . . . 4 | 2. Quantum Information | |||
2.1. Quantum state . . . . . . . . . . . . . . . . . . . . . . 4 | 2.1. Quantum State | |||
2.2. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 5 | 2.2. Qubit | |||
2.3. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 6 | 2.3. Multiple Qubits | |||
3. Entanglement as the fundamental resource . . . . . . . . . . 8 | 3. Entanglement as the Fundamental Resource | |||
4. Achieving quantum connectivity . . . . . . . . . . . . . . . 9 | 4. Achieving Quantum Connectivity | |||
4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 9 | 4.1. Challenges | |||
4.1.1. The measurement problem . . . . . . . . . . . . . . . 9 | 4.1.1. The Measurement Problem | |||
4.1.2. No-cloning theorem . . . . . . . . . . . . . . . . . 10 | 4.1.2. No-Cloning Theorem | |||
4.1.3. Fidelity . . . . . . . . . . . . . . . . . . . . . . 10 | 4.1.3. Fidelity | |||
4.1.4. Inadequacy of direct transmission . . . . . . . . . . 11 | 4.1.4. Inadequacy of Direct Transmission | |||
4.2. Bell pairs . . . . . . . . . . . . . . . . . . . . . . . 11 | 4.2. Bell Pairs | |||
4.3. Teleportation . . . . . . . . . . . . . . . . . . . . . . 12 | 4.3. Teleportation | |||
4.4. The life cycle of entanglement . . . . . . . . . . . . . 13 | 4.4. The Life Cycle of Entanglement | |||
4.4.1. Elementary link generation . . . . . . . . . . . . . 13 | 4.4.1. Elementary Link Generation | |||
4.4.2. Entanglement swapping . . . . . . . . . . . . . . . . 14 | 4.4.2. Entanglement Swapping | |||
4.4.3. Error Management . . . . . . . . . . . . . . . . . . 15 | 4.4.3. Error Management | |||
4.4.4. Delivery . . . . . . . . . . . . . . . . . . . . . . 19 | 4.4.4. Delivery | |||
5. Architecture of a quantum internet . . . . . . . . . . . . . 19 | 5. Architecture of a Quantum Internet | |||
5.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 19 | 5.1. Challenges | |||
5.2. Classical communication . . . . . . . . . . . . . . . . . 21 | 5.2. Classical Communication | |||
5.3. Abstract model of the network . . . . . . . . . . . . . . 22 | 5.3. Abstract Model of the Network | |||
5.3.1. The control and data planes . . . . . . . . . . . . . 22 | 5.3.1. The Control Plane and the Data Plane | |||
5.3.2. Elements of a quantum network . . . . . . . . . . . . 23 | 5.3.2. Elements of a Quantum Network | |||
5.3.3. Putting it all together . . . . . . . . . . . . . . . 24 | 5.3.3. Putting It All Together | |||
5.4. Physical constraints . . . . . . . . . . . . . . . . . . 25 | 5.4. Physical Constraints | |||
5.4.1. Memory lifetimes . . . . . . . . . . . . . . . . . . 26 | 5.4.1. Memory Lifetimes | |||
5.4.2. Rates . . . . . . . . . . . . . . . . . . . . . . . . 26 | 5.4.2. Rates | |||
5.4.3. Communication qubits . . . . . . . . . . . . . . . . 27 | 5.4.3. Communication Qubits | |||
5.4.4. Homogeneity . . . . . . . . . . . . . . . . . . . . . 27 | 5.4.4. Homogeneity | |||
6. Architectural principles . . . . . . . . . . . . . . . . . . 28 | 6. Architectural Principles | |||
6.1. Goals of a quantum internet . . . . . . . . . . . . . . . 28 | 6.1. Goals of a Quantum Internet | |||
6.2. The principles of a quantum internet . . . . . . . . . . 32 | 6.2. The Principles of a Quantum Internet | |||
7. A thought experiment inspired by classical networks . . . . . 34 | 7. A Thought Experiment Inspired by Classical Networks | |||
8. Security Considerations . . . . . . . . . . . . . . . . . . . 36 | 8. Security Considerations | |||
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 36 | 9. IANA Considerations | |||
10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 37 | 10. Informative References | |||
11. Informative References . . . . . . . . . . . . . . . . . . . 37 | Acknowledgements | |||
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 44 | Authors' Addresses | |||
1. Introduction | 1. Introduction | |||
Quantum networks are distributed systems of quantum devices that | Quantum networks are distributed systems of quantum devices that | |||
utilise fundamental quantum mechanical phenomena such as | utilise fundamental quantum mechanical phenomena such as | |||
superposition, entanglement, and quantum measurement to achieve | superposition, entanglement, and quantum measurement to achieve | |||
capabilities beyond what is possible with non-quantum (classical) | capabilities beyond what is possible with non-quantum (classical) | |||
networks [Kimble08]. Depending on the stage of a quantum network | networks [Kimble08]. Depending on the stage of a quantum network | |||
[Wehner18] such devices may range from simple photonic devices | [Wehner18], such devices may range from simple photonic devices | |||
capable of preparing and measuring only one quantum bit (qubit) at a | capable of preparing and measuring only one quantum bit (qubit) at a | |||
time all the way to large-scale quantum computers of the future. A | time all the way to large-scale quantum computers of the future. A | |||
quantum network is not meant to replace classical networks, but | quantum network is not meant to replace classical networks but rather | |||
rather form an overall hybrid classical-quantum network supporting | to form an overall hybrid classical-quantum network supporting new | |||
new capabilities which are otherwise impossible to realise | capabilities that are otherwise impossible to realise [VanMeterBook]. | |||
[VanMeterBook]. For example, the most well-known application of | For example, the most well-known application of quantum | |||
quantum communication, quantum key distribution (QKD), can create and | communication, Quantum Key Distribution (QKD) [QKD], can create and | |||
distribute a pair of symmetric encryption keys in such a way that the | distribute a pair of symmetric encryption keys in such a way that the | |||
security of the entire process relies on the laws of physics (and | security of the entire process relies on the laws of physics (and | |||
thus can be mathematically proven to be unbreakable) rather than the | thus can be mathematically proven to be unbreakable) rather than the | |||
intractability of certain mathematical problems [Bennett14] | intractability of certain mathematical problems [Bennett14] | |||
[Ekert91]. Small networks capable of QKD have even already been | [Ekert91]. Small networks capable of QKD have even already been | |||
deployed at short (roughly 100km) distances [Elliott03] [Peev09] | deployed at short (roughly 100-kilometre) distances [Elliott03] | |||
[Aguado19] [Joshi20]. | [Peev09] [Aguado19] [Joshi20]. | |||
The quantum networking paradigm also offers promise for a range of | The quantum networking paradigm also offers promise for a range of | |||
new applications beyond quantum cryptography, such as distributed | new applications beyond quantum cryptography, such as distributed | |||
quantum computation [Cirac99] [Crepeau02], secure quantum computing | quantum computation [Cirac99] [Crepeau02]; secure quantum computing | |||
in the cloud [Fitzsimons17], quantum-enhanced measurement networks | in the cloud [Fitzsimons17]; quantum-enhanced measurement networks | |||
[Giovanetti04], or higher-precision, long-baseline telescopes | [Giovannetti04]; or higher-precision, long-baseline telescopes | |||
[Gottesman12]. These applications are much more demanding than QKD | [Gottesman12]. These applications are much more demanding than QKD, | |||
and networks capable of executing them are in their infancy. The | and networks capable of executing them are in their infancy. The | |||
first fully quantum, multinode network capable of sending, receiving, | first fully quantum, multinode network capable of sending, receiving, | |||
and manipulating distributed quantum information has only recently | and manipulating distributed quantum information has only recently | |||
been realized [Pompili21.1] | been realised [Pompili21.1]. | |||
Whilst a lot of effort has gone into physically realising and | Whilst a lot of effort has gone into physically realising and | |||
connecting such devices, and making improvements to their speed and | connecting such devices, and making improvements to their speed and | |||
error tolerance, there are no worked out proposals for how to run | error tolerance, no proposals for how to run these networks have been | |||
these networks. To draw an analogy with a classical network, we are | worked out at the time of this writing. To draw an analogy with a | |||
at a stage where we can start to physically connect our devices and | classical network, we are at a stage where we can start to physically | |||
send data, but all sending, receiving, buffer management, connection | connect our devices and send data, but all sending, receiving, buffer | |||
synchronisation, and so on, must be managed by the application | management, connection synchronisation, and so on must be managed by | |||
directly by using low-level, custom-built, and hardware-specific | the application directly by using low-level, custom-built, and | |||
interfaces, rather than being managed by a network stack that exposes | hardware-specific interfaces, rather than being managed by a network | |||
a convenient high-level interface, such as sockets. Only recently, | stack that exposes a convenient high-level interface, such as | |||
was the first ever attempt at such a network stack experimentally | sockets. Only recently was the first-ever attempt at such a network | |||
demonstrated in a laboratory setting [Pompili21.2]. Furthermore, | stack experimentally demonstrated in a laboratory setting | |||
whilst physical mechanisms for transmitting quantum information | [Pompili21.2]. Furthermore, whilst physical mechanisms for | |||
exist, there are no robust protocols for managing such transmissions. | transmitting quantum information exist, there are no robust protocols | |||
for managing such transmissions. | ||||
This document, produced by the Quantum Internet Research Group | This document, produced by the Quantum Internet Research Group | |||
(QIRG), introduces quantum networks and presents general guidelines | (QIRG), introduces quantum networks and presents general guidelines | |||
for the design and construction of such networks. Overall, it is | for the design and construction of such networks. Overall, it is | |||
intended as an introduction to the subject for network engineers and | intended as an introduction to the subject for network engineers and | |||
researchers. It should not be considered as a conclusive statement | researchers. It should not be considered as a conclusive statement | |||
on how quantum network should or will be implemented. This document | on how quantum networks should or will be implemented. This document | |||
was discussed on the QIRG mailing list and several IETF meetings and | was discussed on the QIRG mailing list and several IETF meetings. It | |||
represents the consensus of the QIRG members, both of experts in the | represents the consensus of the QIRG members, of both experts in the | |||
subject matter (from the quantum as well networking domain) as well | subject matter (from the quantum and networking domains) and | |||
as newcomers who are the target audience. | newcomers who are the target audience. | |||
2. Quantum information | 2. Quantum Information | |||
In order to understand the framework for quantum networking, a basic | In order to understand the framework for quantum networking, a basic | |||
understanding of quantum information theory is necessary. The | understanding of quantum information theory is necessary. The | |||
following sections aim to introduce the minimum amount of knowledge | following sections aim to introduce the minimum amount of knowledge | |||
necessary to understand the principles of operation of a quantum | necessary to understand the principles of operation of a quantum | |||
network. This exposition was written with a classical networking | network. This exposition was written with a classical networking | |||
audience in mind. It is assumed that the reader has never before | audience in mind. It is assumed that the reader has never before | |||
been exposed to any quantum physics. We refer the reader to | been exposed to any quantum physics. We refer the reader to | |||
[SutorBook] and [NielsenChuang] for an in-depth introduction to | [SutorBook] and [NielsenChuang] for an in-depth introduction to | |||
quantum information systems. | quantum information systems. | |||
2.1. Quantum state | 2.1. Quantum State | |||
A quantum mechanical system is described by its quantum state. A | A quantum mechanical system is described by its quantum state. A | |||
quantum state is an abstract object that provides a complete | quantum state is an abstract object that provides a complete | |||
description of the system at that particular moment. When combined | description of the system at that particular moment. When combined | |||
with the rules of the system's evolution in time, such as a quantum | with the rules of the system's evolution in time, such as a quantum | |||
circuit, it also then provides a complete description of the system | circuit, it also then provides a complete description of the system | |||
at all times. For the purposes of computing and networking, the | at all times. For the purposes of computing and networking, the | |||
classical equivalent of a quantum state would be a string or stream | classical equivalent of a quantum state would be a string or stream | |||
of logical bit values. These bits provide a complete description of | of logical bit values. These bits provide a complete description of | |||
what values we can read out from that string at that particular | what values we can read out from that string at that particular | |||
moment and when combined with its rules for evolution in time, such | moment, and when combined with its rules for evolution in time, such | |||
as a logical circuit, we will also know its value at any other time. | as a logical circuit, we will also know its value at any other time. | |||
Just like a single classical bit, a quantum mechanical system can be | Just like a single classical bit, a quantum mechanical system can be | |||
simple and consist of a single particle, e.g. an atom or a photon of | simple and consist of a single particle, e.g., an atom or a photon of | |||
light. In this case, the quantum state provides the complete | light. In this case, the quantum state provides the complete | |||
description of that one particle. Similarly, just like a string of | description of that one particle. Similarly, just like a string of | |||
bits consists of multiple bits, a single quantum state can be used to | bits consists of multiple bits, a single quantum state can be used to | |||
also describe an ensemble of many particles. However, because | also describe an ensemble of many particles. However, because | |||
quantum states are governed by the laws of quantum mechanics their | quantum states are governed by the laws of quantum mechanics, their | |||
behaviour is significantly different to that of a string of bits. In | behaviour is significantly different to that of a string of bits. In | |||
this section we will summarise the key concepts to understand these | this section, we will summarise the key concepts to understand these | |||
differences and the we will explain their consequences for networking | differences. We will then explain their consequences for networking | |||
in the rest of the draft. | in the rest of this document. | |||
2.2. Qubit | 2.2. Qubit | |||
The differences between quantum computation and classical computation | The differences between quantum computation and classical computation | |||
begin at the bit-level. A classical computer operates on the binary | begin at the bit level. A classical computer operates on the binary | |||
alphabet { 0, 1 }. A quantum bit, called a qubit, exists over the | alphabet { 0, 1 }. A quantum bit, called a qubit, exists over the | |||
same binary space, but unlike the classical bit, its state can exist | same binary space, but unlike the classical bit, its state can exist | |||
in a superposition of the two possibilities: | in a superposition of the two possibilities: | |||
|qubit> = a |0> + b |1>, | |qubit⟩ = a |0⟩ + b |1⟩, | |||
where |X> is Dirac's ket notation for a quantum state (the value that | where |X⟩ is Dirac's ket notation for a quantum state (the value that | |||
a qubit holds), here the binary 0 and 1, and the coefficients a and b | a qubit holds) -- here, the binary 0 and 1 -- and the coefficients a | |||
are complex numbers called probability amplitudes. Physically, such | and b are complex numbers called probability amplitudes. Physically, | |||
a state can be realised using a variety of different technologies | such a state can be realised using a variety of different | |||
such as electron spin, photon polarisation, atomic energy levels, and | technologies such as electron spin, photon polarisation, atomic | |||
so on. | energy levels, and so on. | |||
Upon measurement, the qubit loses its superposition and irreversibly | Upon measurement, the qubit loses its superposition and irreversibly | |||
collapses into one of the two basis states, either |0> or |1>. Which | collapses into one of the two basis states, either |0⟩ or |1⟩. Which | |||
of the two states it ends up in may not be deterministic, but can be | of the two states it ends up in may not be deterministic but can be | |||
determined from the readout of the measurement. The measurement | determined from the readout of the measurement. The measurement | |||
result is a classical bit, 0 or 1, corresponding to |0> and |1> | result is a classical bit, 0 or 1, corresponding to |0⟩ and |1⟩, | |||
respectively. The probability of measuring the state in the |0> | respectively. The probability of measuring the state in the |0⟩ | |||
state is |a|^2 and similarly the probability of measuring the state | state is |a|^2; similarly, the probability of measuring the state in | |||
in the |1> state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness | the |1⟩ state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness is | |||
is not due to our ignorance of the underlying mechanisms, but rather | not due to our ignorance of the underlying mechanisms but rather is a | |||
is a fundamental feature of a quantum mechanical system [Aspect81]. | fundamental feature of a quantum mechanical system [Aspect81]. | |||
The superposition property plays an important role in fundamental | The superposition property plays an important role in fundamental | |||
gate operations on qubits. Since a qubit can exist in a | gate operations on qubits. Since a qubit can exist in a | |||
superposition of its basis states, the elementary quantum gates are | superposition of its basis states, the elementary quantum gates are | |||
able to act on all states of the superposition at the same time. For | able to act on all states of the superposition at the same time. For | |||
example, consider the NOT gate: | example, consider the NOT gate: | |||
NOT (a |0> + b |1>) -> a |1> + b |0>. | NOT (a |0⟩ + b |1⟩) ➔ a |1⟩ + b |0⟩. | |||
It is important to note that "qubit" can have two meanings. In the | It is important to note that "qubit" can have two meanings. In the | |||
first meaning, "qubit" refers to a physical quantum *system* whose | first meaning, "qubit" refers to a physical quantum *system* whose | |||
quantum state can be expressed as a superposition of two basis | quantum state can be expressed as a superposition of two basis | |||
states, which we often label |0> and |1>. Here, "qubit" refers to a | states, which we often label |0⟩ and |1⟩. Here, "qubit" refers to a | |||
physical implementation akin to what a flip-flop, switch, voltage, or | physical implementation akin to what a flip-flop, switch, voltage, or | |||
current would be for a classical bit. In the second meaning, "qubit" | current would be for a classical bit. In the second meaning, "qubit" | |||
refers to the abstract quantum *state* of a quantum system with such | refers to the abstract quantum *state* of a quantum system with such | |||
two basis states. In this case, the meaning of "qubit" is akin to | two basis states. In this case, the meaning of "qubit" is akin to | |||
the logical value of a bit, from classical computing, i.e. "logical | the logical value of a bit, from classical computing, i.e., "logical | |||
0" or "logical 1". The two concepts are related, because a physical | 0" or "logical 1". The two concepts are related, because a physical | |||
"qubit" (first meaning) can be used to store the abstract "qubit" | "qubit" (first meaning) can be used to store the abstract "qubit" | |||
(second meaning). Both meanings are used interchangeably in | (second meaning). Both meanings are used interchangeably in | |||
literature and the meaning is generally clear from the context. | literature, and the meaning is generally clear from the context. | |||
2.3. Multiple qubits | 2.3. Multiple Qubits | |||
When multiple qubits are combined in a single quantum state the space | When multiple qubits are combined in a single quantum state, the | |||
of possible states grows exponentially and all these states can | space of possible states grows exponentially and all these states can | |||
coexist in a superposition. For example, the general form of a two- | coexist in a superposition. For example, the general form of a two- | |||
qubit register is | qubit register is | |||
a |00> + b |01> + c |10> + d |11> | a |00⟩ + b |01⟩ + c |10⟩ + d |11⟩, | |||
where the coefficients have the same probability amplitude | where the coefficients have the same probability amplitude | |||
interpretation as for the single qubit state. Each state represents | interpretation as for the single-qubit state. Each state represents | |||
a possible outcome of a measurement of the two-qubit register. For | a possible outcome of a measurement of the two-qubit register. For | |||
example, |01> denotes a state in which the first qubit is in the | example, |01⟩ denotes a state in which the first qubit is in the | |||
state |0> and the second is in the state |1>. | state |0⟩ and the second is in the state |1⟩. | |||
Performing single qubit gates affects the relevant qubit in each of | Performing single-qubit gates affects the relevant qubit in each of | |||
the superposition states. Similarly, two-qubit gates also act on all | the superposition states. Similarly, two-qubit gates also act on all | |||
the relevant superposition states, but their outcome is far more | the relevant superposition states, but their outcome is far more | |||
interesting. | interesting. | |||
Consider a two-qubit register where the first qubit is in the | Consider a two-qubit register where the first qubit is in the | |||
superposed state (|0> + |1>)/sqrt(2) and the other is in the | superposed state (|0⟩ + |1⟩)/sqrt(2) and the other is in the | |||
state |0>. This combined state can be written as: | state |0⟩. This combined state can be written as | |||
(|0> + |1>)/sqrt(2) x |0> = (|00> + |10>)/sqrt(2), | (|0⟩ + |1⟩)/sqrt(2) x |0⟩ = (|00⟩ + |10⟩)/sqrt(2), | |||
where x denotes a tensor product (the mathematical mechanism for | where x denotes a tensor product (the mathematical mechanism for | |||
combining quantum states together). | combining quantum states together). | |||
The constant 1/sqrt(2) is called the normalisation factor and | The constant 1/sqrt(2) is called the normalisation factor and | |||
reflects the fact that the probabilities of measuring either a |0> or | reflects the fact that the probabilities of measuring either a |0⟩ or | |||
a |1> for the first qubit add up to one. | a |1⟩ for the first qubit add up to one. | |||
Let us now consider the two-qubit controlled-NOT, or CNOT, gate. The | Let us now consider the two-qubit Controlled NOT, or CNOT, gate. The | |||
CNOT gate takes as input two qubits, a control and target, and | CNOT gate takes as input two qubits -- a control and a target -- and | |||
applies the NOT gate to the target if the control qubit is set. The | applies the NOT gate to the target if the control qubit is set. The | |||
truth table looks like | truth table looks like | |||
+====+=====+ | +====+=====+ | |||
| IN | OUT | | | IN | OUT | | |||
+====+=====+ | +====+=====+ | |||
| 00 | 00 | | | 00 | 00 | | |||
+----+-----+ | +----+-----+ | |||
| 01 | 01 | | | 01 | 01 | | |||
+----+-----+ | +----+-----+ | |||
| 10 | 11 | | | 10 | 11 | | |||
+----+-----+ | +----+-----+ | |||
| 11 | 10 | | | 11 | 10 | | |||
+----+-----+ | +----+-----+ | |||
Table 1 | Table 1: CNOT Truth Table | |||
Now, consider performing a CNOT gate on the state with the first | Now, consider performing a CNOT gate on the state with the first | |||
qubit being the control. We apply a two-qubit gate on all the | qubit being the control. We apply a two-qubit gate on all the | |||
superposition states: | superposition states: | |||
CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2). | CNOT (|00⟩ + |10⟩)/sqrt(2) ➔ (|00⟩ + |11⟩)/sqrt(2). | |||
What is so interesting about this two-qubit gate operation? The | What is so interesting about this two-qubit gate operation? The | |||
final state is *entangled*. There is no possible way of representing | final state is *entangled*. There is no possible way of representing | |||
that quantum state as a product of two individual qubits; they are no | that quantum state as a product of two individual qubits; they are no | |||
longer independent. That is, it is not possible to describe the | longer independent. That is, it is not possible to describe the | |||
quantum state of either of the individual qubits in a way that is | quantum state of either of the individual qubits in a way that is | |||
independent of the other qubit. Only the quantum state of the system | independent of the other qubit. Only the quantum state of the system | |||
that consists of both qubits provides a physically complete | that consists of both qubits provides a physically complete | |||
description of the two-qubit system. The states of the two | description of the two-qubit system. The states of the two | |||
individual qubits are now correlated beyond what is possible to | individual qubits are now correlated beyond what is possible to | |||
achieve classically. Neither qubit is in a definite |0> or |1> | achieve classically. Neither qubit is in a definite |0⟩ or |1⟩ | |||
state, but if we perform a measurement on either one, the outcome of | state, but if we perform a measurement on either one, the outcome of | |||
the partner qubit will *always* yield the exact same outcome. The | the partner qubit will *always* yield the exact same outcome. The | |||
final state, whether it's |00> or |11>, is fundamentally random as | final state, whether it's |00⟩ or |11⟩, is fundamentally random as | |||
before, but the states of the two qubits following a measurement will | before, but the states of the two qubits following a measurement will | |||
always be identical. One can think of this as flipping two coins, | always be identical. One can think of this as flipping two coins, | |||
but the coins always both land on "heads" or both land on "tails" | but both coins always land on "heads" or both land on "tails" | |||
together. Something that we know is impossible classically. | together -- something that we know is impossible classically. | |||
Once a measurement is performed, the two qubits are once again | Once a measurement is performed, the two qubits are once again | |||
independent. The final state is either |00> or |11> and both of | independent. The final state is either |00⟩ or |11⟩, and both of | |||
these states can be trivially decomposed into a product of two | these states can be trivially decomposed into a product of two | |||
individual qubits. The entanglement has been consumed and the | individual qubits. The entanglement has been consumed, and the | |||
entangled state must be prepared again. | entangled state must be prepared again. | |||
3. Entanglement as the fundamental resource | 3. Entanglement as the Fundamental Resource | |||
Entanglement is the fundamental building block of quantum networks. | Entanglement is the fundamental building block of quantum networks. | |||
Consider the state from the previous section: | Consider the state from the previous section: | |||
(|00> + |11>)/sqrt(2). | (|00⟩ + |11⟩)/sqrt(2). | |||
Neither of the two qubits is in a definite |0> or |1> state and we | Neither of the two qubits is in a definite |0⟩ or |1⟩ state, and we | |||
need to know the state of the entire register to be able to fully | need to know the state of the entire register to be able to fully | |||
describe the behaviour of the two qubits. | describe the behaviour of the two qubits. | |||
Entangled qubits have interesting non-local properties. Consider | Entangled qubits have interesting non-local properties. Consider | |||
sending one of the qubits to another device. This device could in | sending one of the qubits to another device. This device could in | |||
principle be anywhere: on the other side of the room, in a different | principle be anywhere: on the other side of the room, in a different | |||
country, or even on a different planet. Provided negligible noise | country, or even on a different planet. Provided negligible noise | |||
has been introduced, the two qubits will forever remain in the | has been introduced, the two qubits will forever remain in the | |||
entangled state until a measurement is performed. The physical | entangled state until a measurement is performed. The physical | |||
distance does not matter at all for entanglement. | distance does not matter at all for entanglement. | |||
skipping to change at page 8, line 36 ¶ | skipping to change at line 368 ¶ | |||
in order to design completely new types of application protocols that | in order to design completely new types of application protocols that | |||
are not possible to achieve with just classical communication. | are not possible to achieve with just classical communication. | |||
Examples of such applications are quantum cryptography [Bennett14] | Examples of such applications are quantum cryptography [Bennett14] | |||
[Ekert91], blind quantum computation [Fitzsimons17], or distributed | [Ekert91], blind quantum computation [Fitzsimons17], or distributed | |||
quantum computation [Crepeau02]. | quantum computation [Crepeau02]. | |||
Entanglement has two very special features from which one can derive | Entanglement has two very special features from which one can derive | |||
some intuition about the types of applications enabled by a quantum | some intuition about the types of applications enabled by a quantum | |||
network. | network. | |||
The first stems from the fact that entanglement enables stronger than | The first stems from the fact that entanglement enables stronger- | |||
classical correlations, leading to opportunities for tasks that | than-classical correlations, leading to opportunities for tasks that | |||
require coordination. As a trivial example, consider the problem of | require coordination. As a trivial example, consider the problem of | |||
consensus between two nodes who want to agree on the value of a | consensus between two nodes who want to agree on the value of a | |||
single bit. They can use the quantum network to prepare the state | single bit. They can use the quantum network to prepare the state | |||
(|00> + |11>)/sqrt(2) with each node holding one of the two qubits. | (|00⟩ + |11⟩)/sqrt(2) with each node holding one of the two qubits. | |||
Once either of the two nodes performs a measurement, the state of the | Once either of the two nodes performs a measurement, the state of the | |||
two qubits collapses to either |00> or |11>, so whilst the outcome is | two qubits collapses to either |00⟩ or |11⟩, so whilst the outcome is | |||
random and does not exist before measurement, the two nodes will | random and does not exist before measurement, the two nodes will | |||
always measure the same value. We can also build the more general | always measure the same value. We can also build the more general | |||
multi-qubit state (|00...> + |11...>)/sqrt(2) and perform the same | multi-qubit state (|00...⟩ + |11...⟩)/sqrt(2) and perform the same | |||
algorithm between an arbitrary number of nodes. These stronger than | algorithm between an arbitrary number of nodes. These stronger-than- | |||
classical correlations generalise to more complicated measurement | classical correlations generalise to measurement schemes that are | |||
schemes as well. | more complicated as well. | |||
The second feature of entanglement is that it cannot be shared, in | The second feature of entanglement is that it cannot be shared, in | |||
the sense that if two qubits are maximally entangled with each other, | the sense that if two qubits are maximally entangled with each other, | |||
then it is physically impossible for these two qubits to also be | then it is physically impossible for these two qubits to also be | |||
entangled with a third qubit [Terhal04]. Hence, entanglement forms a | entangled with a third qubit [Terhal04]. Hence, entanglement forms a | |||
sort of private and inherently untappable connection between two | sort of private and inherently untappable connection between two | |||
nodes once established. | nodes once established. | |||
Entanglement is created through local interactions between two qubits | Entanglement is created through local interactions between two qubits | |||
or as a product of the way the qubits were created (e.g. entangled | or as a product of the way the qubits were created (e.g., entangled | |||
photon pairs). To create a distributed entangled state, one can then | photon pairs). To create a distributed entangled state, one can then | |||
physically send one of the qubits to a remote node. It is also | physically send one of the qubits to a remote node. It is also | |||
possible to directly entangle qubits that are physically separated, | possible to directly entangle qubits that are physically separated, | |||
but this still requires local interactions between some other qubits | but this still requires local interactions between some other qubits | |||
that the separated qubits are initially entangled with. Therefore, | that the separated qubits are initially entangled with. Therefore, | |||
it is the transmission of qubits that draws the line between a | it is the transmission of qubits that draws the line between a | |||
genuine quantum network and a collection of quantum computers | genuine quantum network and a collection of quantum computers | |||
connected over a classical network. | connected over a classical network. | |||
A quantum network is defined as a collection of nodes that is able to | A quantum network is defined as a collection of nodes that is able to | |||
exchange qubits and distribute entangled states amongst themselves. | exchange qubits and distribute entangled states amongst themselves. | |||
A quantum node that is able only to communicate classically with | A quantum node that is able only to communicate classically with | |||
another quantum node is not a member of a quantum network. | another quantum node is not a member of a quantum network. | |||
More complex services and applications can be built on top of | Services and applications that are more complex can be built on top | |||
entangled states distributed by the network, see e.g. [ZOO] | of entangled states distributed by the network; for example, see | |||
[ZOO]. | ||||
4. Achieving quantum connectivity | 4. Achieving Quantum Connectivity | |||
This section explains the meaning of quantum connectivity and the | This section explains the meaning of quantum connectivity and the | |||
necessary physical processes at an abstract level. | necessary physical processes at an abstract level. | |||
4.1. Challenges | 4.1. Challenges | |||
A quantum network cannot be built by simply extrapolating all the | A quantum network cannot be built by simply extrapolating all the | |||
classical models to their quantum analogues. Sending qubits over a | classical models to their quantum analogues. Sending qubits over a | |||
wire like we send classical bits is simply not as easy to do. There | wire like we send classical bits is simply not as easy to do. There | |||
are several technological as well as fundamental challenges that make | are several technological as well as fundamental challenges that make | |||
classical approaches unsuitable in a quantum context. | classical approaches unsuitable in a quantum context. | |||
4.1.1. The measurement problem | 4.1.1. The Measurement Problem | |||
In classical computers and networks we can read out the bits stored | In classical computers and networks, we can read out the bits stored | |||
in memory at any time. This is helpful for a variety of purposes | in memory at any time. This is helpful for a variety of purposes | |||
such as copying, error detection and correction, and so on. This is | such as copying, error detection and correction, and so on. This is | |||
not possible with qubits. | not possible with qubits. | |||
A measurement of a qubit's state will destroy its superposition and | A measurement of a qubit's state will destroy its superposition and | |||
with it any entanglement it may have been part of. Once a qubit is | with it any entanglement it may have been part of. Once a qubit is | |||
being processed, it cannot be read out until a suitable point in the | being processed, it cannot be read out until a suitable point in the | |||
computation, determined by the protocol handling the qubit, has been | computation, determined by the protocol handling the qubit, has been | |||
reached. Therefore, we cannot use the same methods known from | reached. Therefore, we cannot use the same methods known from | |||
classical computing for the purposes of error detection and | classical computing for the purposes of error detection and | |||
correction. Nevertheless, quantum error detection and correction | correction. Nevertheless, quantum error detection and correction | |||
schemes exist that take this problem into account and how a network | schemes exist that take this problem into account, and how a network | |||
chooses to manage errors will have an impact on its architecture. | chooses to manage errors will have an impact on its architecture. | |||
4.1.2. No-cloning theorem | 4.1.2. No-Cloning Theorem | |||
Since directly reading the state of a qubit is not possible, one | Since directly reading the state of a qubit is not possible, one | |||
could ask if we can simply copy a qubit without looking at it. | could ask if we can simply copy a qubit without looking at it. | |||
Unfortunately, this is fundamentally not possible in quantum | Unfortunately, this is fundamentally not possible in quantum | |||
mechanics [Park70] [Wootters82]. | mechanics [Park70] [Wootters82]. | |||
The no-cloning theorem states that it is impossible to create an | The no-cloning theorem states that it is impossible to create an | |||
identical copy of an arbitrary, unknown quantum state. Therefore, it | identical copy of an arbitrary, unknown quantum state. Therefore, it | |||
is also impossible to use the same mechanisms that worked for | is also impossible to use the same mechanisms that worked for | |||
classical networks for signal amplification, retransmission, and so | classical networks for signal amplification, retransmission, and so | |||
on as they all rely on the ability to copy the underlying data. | on, as they all rely on the ability to copy the underlying data. | |||
Since any physical channel will always be lossy, connecting nodes | Since any physical channel will always be lossy, connecting nodes | |||
within a quantum network is a challenging endeavour and its | within a quantum network is a challenging endeavour, and its | |||
architecture must at its core address this very issue. | architecture must at its core address this very issue. | |||
4.1.3. Fidelity | 4.1.3. Fidelity | |||
In general, it is expected that a classical packet arrives at its | In general, it is expected that a classical packet arrives at its | |||
destination without any errors introduced by hardware noise along the | destination without any errors introduced by hardware noise along the | |||
way. This is verified at various levels through a variety of error | way. This is verified at various levels through a variety of error | |||
detection and correction mechanisms. Since we cannot read or copy a | detection and correction mechanisms. Since we cannot read or copy a | |||
quantum state, error detection and correction is more involved. | quantum state, error detection and correction are more involved. | |||
To describe the quality of a quantum state, a physical quantity | To describe the quality of a quantum state, a physical quantity | |||
called fidelity is used [NielsenChuang]. Fidelity takes a value | called fidelity is used [NielsenChuang]. Fidelity takes a value | |||
between 0 and 1 -- higher is better, and less than 0.5 means the | between 0 and 1 -- higher is better, and less than 0.5 means the | |||
state is unusable. It measures how close a quantum state is to the | state is unusable. It measures how close a quantum state is to the | |||
state we have tried to create. It expresses the probability that the | state we have tried to create. It expresses the probability that the | |||
state will behave exactly the same as our desired state. Fidelity is | state will behave exactly the same as our desired state. Fidelity is | |||
an important property of a quantum system that allows us to quantify | an important property of a quantum system that allows us to quantify | |||
how much a particular state has been affected by noise from various | how much a particular state has been affected by noise from various | |||
sources (gate errors, channel losses, environment noise). | sources (gate errors, channel losses, environment noise). | |||
Interestingly, quantum applications do not need perfect fidelity to | Interestingly, quantum applications do not need perfect fidelity to | |||
be able to execute -- as long as the fidelity is above some | be able to execute -- as long as the fidelity is above some | |||
application-specific threshold, they will simply operate at lower | application-specific threshold, they will simply operate at lower | |||
rates. Therefore, rather than trying to ensure that we always | rates. Therefore, rather than trying to ensure that we always | |||
deliver perfect states (a technologically challenging task) | deliver perfect states (a technologically challenging task), | |||
applications will specify a minimum threshold for the fidelity and | applications will specify a minimum threshold for the fidelity, and | |||
the network will try its best to deliver it. A higher fidelity can | the network will try its best to deliver it. A higher fidelity can | |||
be achieved by either having hardware produce states of better | be achieved by either having hardware produce states of better | |||
fidelity (sometimes one can sacrifice rate for higher fidelity) or by | fidelity (sometimes one can sacrifice rate for higher fidelity) or | |||
employing quantum error detection and correction mechanisms (see | employing quantum error detection and correction mechanisms (see | |||
[Mural16] and [VanMeterBook] chapter 11). | [Mural16] and Chapter 11 of [VanMeterBook]). | |||
4.1.4. Inadequacy of direct transmission | 4.1.4. Inadequacy of Direct Transmission | |||
Conceptually, the most straightforward way to distribute an entangled | Conceptually, the most straightforward way to distribute an entangled | |||
state is to simply transmit one of the qubits directly to the other | state is to simply transmit one of the qubits directly to the other | |||
end across a series of nodes while performing sufficient forward | end across a series of nodes while performing sufficient forward | |||
quantum error correction (Section 4.4.3.2) to bring losses down to an | Quantum Error Correction (QEC) (Section 4.4.3.2) to bring losses down | |||
acceptable level. Despite the no-cloning theorem and the inability | to an acceptable level. Despite the no-cloning theorem and the | |||
to directly measure a quantum state, error-correcting mechanisms for | inability to directly measure a quantum state, error-correcting | |||
quantum communication exist [Jiang09] [Fowler10] [Devitt13] | mechanisms for quantum communication exist [Jiang09] [Fowler10] | |||
[Mural16]. However, quantum error correction makes very high demands | [Devitt13] [Mural16]. However, QEC makes very high demands on both | |||
on both resources (physical qubits needed) and their initial | resources (physical qubits needed) and their initial fidelity. | |||
fidelity. Implementation is very challenging and quantum error | Implementation is very challenging, and QEC is not expected to be | |||
correction is not expected to be used until later generations of | used until later generations of quantum networks are possible (see | |||
quantum networks are possible (see [Mural16] figure 2 and | Figure 2 of [Mural16] and Section 4.4.3.3 of this document). Until | |||
Section 4.4.3.3). Until then, quantum networks rely on entanglement | then, quantum networks rely on entanglement swapping (Section 4.4.2) | |||
swapping (Section 4.4.2) and teleportation (Section 4.3). This | and teleportation (Section 4.3). This alternative relies on the | |||
alternative relies on the observation that we do not need to be able | observation that we do not need to be able to distribute any | |||
to distribute any arbitrary entangled quantum state. We only need to | arbitrary entangled quantum state. We only need to be able to | |||
be able to distribute any one of what are known as the Bell pair | distribute any one of what are known as the Bell pair states | |||
states [Briegel98]. | [Briegel98]. | |||
4.2. Bell pairs | 4.2. Bell Pairs | |||
Bell pair states are the entangled two-qubit states: | Bell pair states are the entangled two-qubit states: | |||
|00> + |11>, |00> - |11>, |01> + |10>, |01> - |10>, | |00⟩ + |11⟩, | |||
|00⟩ - |11⟩, | ||||
|01⟩ + |10⟩, | ||||
|01⟩ - |10⟩, | ||||
where the constant 1/sqrt(2) normalisation factor has been ignored | where the constant 1/sqrt(2) normalisation factor has been ignored | |||
for clarity. Any of the four Bell pair states above will do, as it | for clarity. Any of the four Bell pair states above will do, as it | |||
is possible to transform any Bell pair into another Bell pair with | is possible to transform any Bell pair into another Bell pair with | |||
local operations performed on only one of the qubits. When each | local operations performed on only one of the qubits. When each | |||
qubit in a Bell pair is held by a separate node, either node can | qubit in a Bell pair is held by a separate node, either node can | |||
apply a series of single qubit gates to their qubit alone in order to | apply a series of single-qubit gates to their qubit alone in order to | |||
transform the state between the different variants. | transform the state between the different variants. | |||
Distributing a Bell pair between two nodes is much easier than | Distributing a Bell pair between two nodes is much easier than | |||
transmitting an arbitrary quantum state over a network. Since the | transmitting an arbitrary quantum state over a network. Since the | |||
state is known, handling errors becomes easier and small-scale error- | state is known, handling errors becomes easier, and small-scale error | |||
correction (such as entanglement distillation discussed in a later | correction (such as entanglement distillation, as discussed in | |||
section) combined with reattempts becomes a valid strategy. | Section 4.4.3.1), combined with reattempts, becomes a valid strategy. | |||
The reason for using Bell pairs specifically as opposed to any other | The reason for using Bell pairs specifically as opposed to any other | |||
two-qubit state is that they are the maximally entangled two-qubit | two-qubit state is that they are the maximally entangled two-qubit | |||
set of basis states. Maximal entanglement means that these states | set of basis states. Maximal entanglement means that these states | |||
have the strongest non-classical correlations of all possible two- | have the strongest non-classical correlations of all possible two- | |||
qubit states. Furthermore, since single-qubit local operations can | qubit states. Furthermore, since single-qubit local operations can | |||
never increase entanglement, less entangled states would impose some | never increase entanglement, states that are less entangled would | |||
constraints on distributed quantum algorithms. This makes Bell pairs | impose some constraints on distributed quantum algorithms. This | |||
particularly useful as a generic building block for distributed | makes Bell pairs particularly useful as a generic building block for | |||
quantum applications. | distributed quantum applications. | |||
4.3. Teleportation | 4.3. Teleportation | |||
The observation that we only need to be able to distribute Bell pairs | The observation that we only need to be able to distribute Bell pairs | |||
relies on the fact that this enables the distribution of any other | relies on the fact that this enables the distribution of any other | |||
arbitrary entangled state. This can be achieved via quantum state | arbitrary entangled state. This can be achieved via quantum state | |||
teleportation [Bennett93]. Quantum state teleportation consumes an | teleportation [Bennett93]. Quantum state teleportation consumes an | |||
unknown qubit state that we want to transmit and recreates it at the | unknown qubit state that we want to transmit and recreates it at the | |||
desired destination. This does not violate the no-cloning theorem as | desired destination. This does not violate the no-cloning theorem, | |||
the original state is destroyed in the process. | as the original state is destroyed in the process. | |||
To achieve this, an entangled pair needs to be distributed between | To achieve this, an entangled pair needs to be distributed between | |||
the source and destination before teleportation commences. The | the source and destination before teleportation commences. The | |||
source then entangles the transmission qubit with its end of the pair | source then entangles the transmission qubit with its end of the pair | |||
and performs a read out of the two qubits (the sum of these | and performs a readout of the two qubits (the sum of these operations | |||
operations is called a Bell state measurement). This consumes the | is called a Bell state measurement). This consumes the Bell pair's | |||
Bell pair's entanglement, turning the source and destination qubits | entanglement, turning the source and destination qubits into | |||
into independent states. The measurements yields two classical bits | independent states. The measurement yields two classical bits, which | |||
which the source sends to the destination over a classical channel. | the source sends to the destination over a classical channel. Based | |||
Based on the value of the received two classical bits, the | on the value of the received two classical bits, the destination | |||
destination performs one of four possible corrections (called the | performs one of four possible corrections (called the Pauli | |||
Pauli corrections) on its end of the pair, which turns it into the | corrections) on its end of the pair, which turns it into the unknown | |||
unknown qubit state that we wanted to transmit. This requirement to | qubit state that we wanted to transmit. This requirement to | |||
communicate the measurement read out over a classical channel | communicate the measurement readout over a classical channel | |||
unfortunately means that entanglement cannot be used to transmit | unfortunately means that entanglement cannot be used to transmit | |||
information faster than the speed of light. | information faster than the speed of light. | |||
The unknown quantum state that was transmitted was never fed into the | The unknown quantum state that was transmitted was never fed into the | |||
network itself. Therefore, the network needs to only be able to | network itself. Therefore, the network needs to only be able to | |||
reliably produce Bell pairs between any two nodes in the network. | reliably produce Bell pairs between any two nodes in the network. | |||
Thus, a key difference between a classical and quantum data planes is | Thus, a key difference between a classical data plane and a quantum | |||
that a classical one carries user data, but a quantum data plane | data plane is that a classical data plane carries user data but a | |||
provides the resources for the user to transmit user data themselves | quantum data plane provides the resources for the user to transmit | |||
without further involvement of the network. | user data themselves without further involvement of the network. | |||
4.4. The life cycle of entanglement | 4.4. The Life Cycle of Entanglement | |||
Reducing the problem of quantum connectivity to one of generating a | Reducing the problem of quantum connectivity to one of generating a | |||
Bell pair has facilitated the problem, but it has not solved it. In | Bell pair has reduced the problem to a simpler, more fundamental | |||
this section, we discuss how these entangled pairs are generated in | case, but it has not solved it. In this section, we discuss how | |||
the first place, and how their two qubits are delivered to the end- | these entangled pairs are generated in the first place and how their | |||
points. | two qubits are delivered to the end-points. | |||
4.4.1. Elementary link generation | 4.4.1. Elementary Link Generation | |||
In a quantum network, entanglement is always first generated locally | In a quantum network, entanglement is always first generated locally | |||
(at a node or an auxiliary element) followed by a movement of one or | (at a node or an auxiliary element), followed by a movement of one or | |||
both of the entangled qubits across the link through quantum | both of the entangled qubits across the link through quantum | |||
channels. In this context, photons (particles of light) are the | channels. In this context, photons (particles of light) are the | |||
natural candidate for entanglement carriers, called flying qubits. | natural candidate for entanglement carriers. Because these photons | |||
The rationale for this choice is related to the advantages provided | carry quantum states from place to place at high speed, we call them | |||
by photons such as moderate interaction with the environment leading | flying qubits. The rationale for this choice is related to the | |||
to moderate decoherence, convenient control with standard optical | advantages provided by photons, such as moderate interaction with the | |||
components, and high-speed, low-loss transmissions. However, since | environment leading to moderate decoherence; convenient control with | |||
photons are hard to store, a transducer must transfer the flying | standard optical components; and high-speed, low-loss transmissions. | |||
qubit's state to a qubit suitable for information processing and/or | However, since photons are hard to store, a transducer must transfer | |||
storage (often referred to as a matter qubit). | the flying qubit's state to a qubit suitable for information | |||
processing and/or storage (often referred to as a matter qubit). | ||||
Since this process may fail, in order to generate and store | Since this process may fail, in order to generate and store | |||
entanglement efficiently, we must be able to distinguish successful | entanglement efficiently, we must be able to distinguish successful | |||
attempts from failures. Entanglement generation schemes that are | attempts from failures. Entanglement generation schemes that are | |||
able to announce successful generation are called heralded | able to announce successful generation are called heralded | |||
entanglement generation schemes. | entanglement generation schemes. | |||
There exist three basic schemes for heralded entanglement generation | There exist three basic schemes for heralded entanglement generation | |||
on a link through coordinated action of the two nodes at the two ends | on a link through coordinated action of the two nodes at the two ends | |||
of the link [Cacciapuoti19]: | of the link [Cacciapuoti19]: | |||
* "At mid-point": in this scheme an entangled photon pair source | "At mid-point": In this scheme, an entangled photon pair source | |||
sitting midway between the two nodes with matter qubits sends an | sitting midway between the two nodes with matter qubits sends an | |||
entangled photon through a quantum channel to each of the nodes. | entangled photon through a quantum channel to each of the nodes. | |||
There, transducers are invoked to transfer the entanglement from | There, transducers are invoked to transfer the entanglement from | |||
the flying qubits to the matter qubits. In this scheme, the | the flying qubits to the matter qubits. In this scheme, the | |||
transducers know if the transfers succeeded and are able to herald | transducers know if the transfers succeeded and are able to herald | |||
successful entanglement generation via a message exchange over the | successful entanglement generation via a message exchange over the | |||
classical channel. | classical channel. | |||
* "At source": in this scheme one of the two nodes sends a flying | "At source": In this scheme, one of the two nodes sends a flying | |||
qubit that is entangled with one of its matter qubits. A | qubit that is entangled with one of its matter qubits. A | |||
transducer at the other end of the link will transfer the | transducer at the other end of the link will transfer the | |||
entanglement from the flying qubit to one of its matter qubits. | entanglement from the flying qubit to one of its matter qubits. | |||
Just like in the previous scheme, the transducer knows if its | Just like in the previous scheme, the transducer knows if its | |||
transfer succeeded and is able to herald successful entanglement | transfer succeeded and is able to herald successful entanglement | |||
generation with a classical message sent to the other node. | generation with a classical message sent to the other node. | |||
* "At both end-points": in this scheme both nodes send a flying | "At both end-points": In this scheme, both nodes send a flying qubit | |||
qubit that is entangled with one of their matter qubits. A | that is entangled with one of their matter qubits. A detector | |||
detector somewhere in between the nodes performs a joint | somewhere in between the nodes performs a joint measurement on the | |||
measurement on the two qubits, which stochastically projects the | flying qubits, which stochastically projects the remote matter | |||
remote matter qubits into an entangled quantum state. The | qubits into an entangled quantum state. The detector knows if the | |||
detector knows if the entanglement succeeded and is able to herald | entanglement succeeded and is able to herald successful | |||
successful entanglement generation by sending a message to each | entanglement generation by sending a message to each node over the | |||
node over the classical channel. | classical channel. | |||
The "mid-point source" scheme is more robust to photon loss, but in | The "mid-point source" scheme is more robust to photon loss, but in | |||
the other schemes the nodes retain greater control over the entangled | the other schemes, the nodes retain greater control over the | |||
pair generation. | entangled pair generation. | |||
Note that whilst photons travel in a particular direction through the | Note that whilst photons travel in a particular direction through the | |||
quantum channel the resulting entangled pair of qubits does not have | quantum channel the resulting entangled pair of qubits does not have | |||
a direction associated with it. Physically, there is no upstream or | a direction associated with it. Physically, there is no upstream or | |||
downstream end of the pair. | downstream end of the pair. | |||
4.4.2. Entanglement swapping | 4.4.2. Entanglement Swapping | |||
The problem with generating entangled pairs directly across a link is | The problem with generating entangled pairs directly across a link is | |||
that efficiency decreases with channel length. Beyond a few 10s of | that efficiency decreases with channel length. Beyond a few tens of | |||
kilometres in optical fibre or 1000 kilometres in free space (via | kilometres in optical fibre or 1000 kilometres in free space (via | |||
satellite) the rate is effectively zero and due to the no-cloning | satellite), the rate is effectively zero, and due to the no-cloning | |||
theorem we cannot simply amplify the signal. The solution is | theorem we cannot simply amplify the signal. The solution is | |||
entanglement swapping [Briegel98]. | entanglement swapping [Briegel98]. | |||
A Bell pair between any two nodes in the network can be constructed | A Bell pair between any two nodes in the network can be constructed | |||
by combining the pairs generated along each individual link on a path | by combining the pairs generated along each individual link on a path | |||
between the two end-points. Each node along the path can consume the | between the two end-points. Each node along the path can consume the | |||
two pairs on the two links that it is connected to in order to | two pairs on the two links to which it is connected, in order to | |||
produce a new entangled pair between the two remote ends. This | produce a new entangled pair between the two remote ends. This | |||
process is known as entanglement swapping. Pictorially it can be | process is known as entanglement swapping. It can be represented | |||
represented as follows: | pictorially as follows: | |||
+---------+ +---------+ +---------+ | +---------+ +---------+ +---------+ | |||
| A | | B | | C | | | A | | B | | C | | |||
| |------| |------| | | | |------| |------| | | |||
| X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 | | | X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 | | |||
+---------+ +---------+ +---------+ | +---------+ +---------+ +---------+ | |||
where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2 | where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2 | |||
are the qubits of entangled pair Y. The entanglement is denoted with | are the qubits of entangled pair Y. The entanglement is denoted with | |||
~~. In the diagram above, nodes A and B share the pair X and nodes B | ~~. In the diagram above, nodes A and B share the pair X and nodes B | |||
and C share the pair Y, but we want entanglement between A and C. | and C share the pair Y, but we want entanglement between A and C. | |||
To achieve this goal, we simply teleport the qubit X2 using the pair | To achieve this goal, we simply teleport the qubit X2 using the pair | |||
Y. This requires node B to perform a Bell state measurement on the | Y. This requires node B to perform a Bell state measurement on the | |||
qubits X2 and Y1 which result in the destruction of the entanglement | qubits X2 and Y1 that results in the destruction of the entanglement | |||
between Y1 and Y2. However, X2 is recreated in Y2's place, carrying | between Y1 and Y2. However, X2 is recreated in Y2's place, carrying | |||
with it its entanglement with X1. The end-result is shown below: | with it its entanglement with X1. The end result is shown below: | |||
+---------+ +---------+ +---------+ | +---------+ +---------+ +---------+ | |||
| A | | B | | C | | | A | | B | | C | | |||
| |------| |------| | | | |------| |------| | | |||
| X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 | | | X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 | | |||
+---------+ +---------+ +---------+ | +---------+ +---------+ +---------+ | |||
Depending on the needs of the network and/or application, a final | Depending on the needs of the network and/or application, a final | |||
Pauli correction at the recipient node may not be necessary since the | Pauli correction at the recipient node may not be necessary, since | |||
result of this operation is also a Bell pair. However, the two | the result of this operation is also a Bell pair. However, the two | |||
classical bits that form the read out from the measurement at node B | classical bits that form the readout from the measurement at node B | |||
must still be communicated, because they carry information about | must still be communicated, because they carry information about | |||
which of the four Bell pairs was actually produced. If a correction | which of the four Bell pairs was actually produced. If a correction | |||
is not performed, the recipient must be informed which Bell pair was | is not performed, the recipient must be informed which Bell pair was | |||
received. | received. | |||
This process of teleporting Bell pairs using other entangled pairs is | This process of teleporting Bell pairs using other entangled pairs is | |||
called entanglement swapping. Quantum nodes that create long- | called entanglement swapping. Quantum nodes that create long- | |||
distance entangled pairs via entanglement swapping are called quantum | distance entangled pairs via entanglement swapping are called quantum | |||
repeaters in academic literature [Briegel98] and we will use the same | repeaters in academic literature [Briegel98]. We will use the same | |||
terminology in this draft. | terminology in this document. | |||
4.4.3. Error Management | 4.4.3. Error Management | |||
4.4.3.1. Distillation | 4.4.3.1. Distillation | |||
Neither the generation of Bell pairs nor the swapping operations are | Neither the generation of Bell pairs nor the swapping operations are | |||
noiseless operations. Therefore, with each link and each swap the | noiseless operations. Therefore, with each link and each swap, the | |||
fidelity of the state degrades. However, it is possible to create | fidelity of the state degrades. However, it is possible to create | |||
higher fidelity Bell pair states from two or more lower fidelity | higher-fidelity Bell pair states from two or more lower-fidelity | |||
pairs through a process called distillation (sometimes also referred | pairs through a process called distillation (sometimes also referred | |||
to as purification) [Dur07]. | to as purification) [Dur07]. | |||
To distil a quantum state, a second (and sometimes third) quantum | To distil a quantum state, a second (and sometimes third) quantum | |||
state is used as a "test tool" to test a proposition about the first | state is used as a "test tool" to test a proposition about the first | |||
state, e.g., "the parity of the two qubits in the first state is | state, e.g., "the parity of the two qubits in the first state is | |||
even." When the test succeeds, confidence in the state is improved, | even." When the test succeeds, confidence in the state is improved, | |||
and thus the fidelity is improved. The test tool states are | and thus the fidelity is improved. The test tool states are | |||
destroyed in the process, so resource demands increase substantially | destroyed in the process, so resource demands increase substantially | |||
when distillation is used. When the test fails, the tested state | when distillation is used. When the test fails, the tested state | |||
must also be discarded. Distillation makes low demands on fidelity | must also be discarded. Distillation makes low demands on fidelity | |||
and resources compared to quantum error correction, but distributed | and resources compared to QEC, but distributed protocols incur round- | |||
protocols incur round-trip delays due to classical communication | trip delays due to classical communication [Bennett96]. | |||
[Bennett96]. | ||||
4.4.3.2. Quantum Error Correction | 4.4.3.2. Quantum Error Correction (QEC) | |||
Just like classical error correction, quantum error correction (QEC) | Just like classical error correction, QEC encodes logical qubits | |||
encodes logical qubits using several physical (raw) qubits to protect | using several physical (raw) qubits to protect them from the errors | |||
them from errors described in Section 4.1.3 [Jiang09] [Fowler10] | described in Section 4.1.3 [Jiang09] [Fowler10] [Devitt13] [Mural16]. | |||
[Devitt13] [Mural16]. Furthermore, similarly to its classical | Furthermore, similarly to its classical counterpart, QEC can not only | |||
counterpart, QEC can not only correct state errors but also account | correct state errors but also account for lost qubits. Additionally, | |||
for lost qubits. Additionally, if all physical qubits which encode a | if all physical qubits that encode a logical qubit are located at the | |||
logical qubit are located at the same node, the correction procedure | same node, the correction procedure can be executed locally, even if | |||
can be executed locally, even if the logical qubit is entangled with | the logical qubit is entangled with remote qubits. | |||
remote qubits. | ||||
Although QEC was originally a scheme proposed to protect a qubit from | Although QEC was originally a scheme proposed to protect a qubit from | |||
noise, QEC can also be applied to entanglement distillation. Such | noise, QEC can also be applied to entanglement distillation. Such | |||
QEC-applied distillation is cost-effective but requires a higher base | QEC-applied distillation is cost effective but requires a higher base | |||
fidelity. | fidelity. | |||
4.4.3.3. Error management schemes | 4.4.3.3. Error Management Schemes | |||
Quantum networks have been categorized into three "generations" based | Quantum networks have been categorised into three "generations" based | |||
on the error management scheme they employ [Mural16]. Note that | on the error management scheme they employ [Mural16]. Note that | |||
these "generations" are more like categories; they do not necessarily | these "generations" are more like categories; they do not necessarily | |||
imply a time progression and do not obsolete each other, though the | imply a time progression and do not obsolete each other, though the | |||
later generations do require more advanced technologies. Which | later generations do require technologies that are more advanced. | |||
generation is used depends on the hardware platform and network | Which generation is used depends on the hardware platform and network | |||
design choices. | design choices. | |||
Table 2 summarises the generations. | Table 2 summarises the generations. | |||
+===========+=================+=======================+============+ | +===========+================+=======================+=============+ | |||
| | First | Second generation | Third | | | | First | Second generation | Third | | |||
| | generation | | generation | | | | generation | | generation | | |||
+===========+=================+=======================+============+ | +===========+================+=======================+=============+ | |||
| Loss | Heralded | Heralded entanglement | Quantum | | | Loss | Heralded | Heralded entanglement | QEC (no | | |||
| tolerance | entanglement | generation (bi- | Error | | | tolerance | entanglement | generation | classical | | |||
| | generation (bi- | directional classical | Correction | | | | generation | (bidirectional | signalling) | | |||
| | directional | signaling) | (no | | | | (bidirectional | classical signalling) | | | |||
| | classical | | classical | | | | classical | | | | |||
| | signaling) | | signaling) | | | | signalling) | | | | |||
+-----------+-----------------+-----------------------+------------+ | +-----------+----------------+-----------------------+-------------+ | |||
+-----------+-----------------+-----------------------+------------+ | +-----------+----------------+-----------------------+-------------+ | |||
| Error | Entanglement | Entanglement | Quantum | | | Error | Entanglement | Entanglement | QEC (no | | |||
| tolerance | distillation | distillation (uni- | Error | | | tolerance | distillation | distillation | classical | | |||
| | (bi-directional | directional classical | Correction | | | | (bidirectional | (unidirectional | signalling) | | |||
| | classical | signaling) or Quantum | (no | | | | classical | classical signalling) | | | |||
| | signaling) | Error Correction (no | classical | | | | signalling) | or QEC (no classical | | | |||
| | | classical signaling) | signaling) | | | | | signalling) | | | |||
+-----------+-----------------+-----------------------+------------+ | +-----------+----------------+-----------------------+-------------+ | |||
Table 2: Classical signaling and generations | Table 2: Classical Signalling and Generations | |||
Generations are defined by the directions of classical signalling | Generations are defined by the directions of classical signalling | |||
required in their distributed protocols for loss tolerance and error | required in their distributed protocols for loss tolerance and error | |||
tolerance. Classical signalling carries the classical bits and | tolerance. Classical signalling carries the classical bits, | |||
incurs round-trip delays described in Section 4.4.3.1, hence they | incurring round-trip delays. As described in Section 4.4.3.1, these | |||
affect the performance of quantum networks, especially as the | delays affect the performance of quantum networks, especially as the | |||
distance between the communicating nodes increases. | distance between the communicating nodes increases. | |||
Loss tolerance is about tolerating qubit transmission losses between | Loss tolerance is about tolerating qubit transmission losses between | |||
nodes. Heralded entanglement generation, as described in | nodes. Heralded entanglement generation, as described in | |||
Section 4.4.1, confirms the receipt of an entangled qubit using a | Section 4.4.1, confirms the receipt of an entangled qubit using a | |||
heralding signal. A pair of directly connected quantum nodes | heralding signal. A pair of directly connected quantum nodes | |||
repeatedly attempt to generate an entangled pair until the a | repeatedly attempt to generate an entangled pair until the heralding | |||
heralding signal is received. As described in Section 4.4.3.2, QEC | signal is received. As described in Section 4.4.3.2, QEC can be | |||
can be applied to complement lost qubits eliminating the need for re- | applied to complement lost qubits, eliminating the need for | |||
attempts. Furthermore, since the correction procedure is composed of | reattempts. Furthermore, since the correction procedure is composed | |||
local operations, it does not require a heralding signal. However, | of local operations, it does not require a heralding signal. | |||
it is possible only when the photon loss rate from transmission to | However, it is possible only when the photon loss rate from | |||
measurement is less than 50%. | transmission to measurement is less than 50%. | |||
Error tolerance is about tolerating quantum state errors. | Error tolerance is about tolerating quantum state errors. | |||
Entanglement distillation is the easiest mechanism for improved error | Entanglement distillation is the easiest mechanism to implement for | |||
tolerance to implement, but it incurs round-trip delays due the | improved error tolerance, but it incurs round-trip delays due to the | |||
requirement for bi-directional classical signalling. The | requirement for bidirectional classical signalling. The alternative, | |||
alternative, QEC, is able to correct state errors locally so that it | QEC, is able to correct state errors locally so that it does not need | |||
does not need any classical signalling between the quantum nodes. In | any classical signalling between the quantum nodes. In between these | |||
between these two extremes, there is also QEC-applied distillation, | two extremes, there is also QEC-applied distillation, which requires | |||
which requires uni-directional classical signalling. | unidirectional classical signalling. | |||
The three "generations" summarised: | The three "generations" summarised: | |||
1. First generation quantum networks use heralding for loss | 1. First-generation quantum networks use heralding for loss | |||
tolerance and entanglement distillation for error tolerance. | tolerance and entanglement distillation for error tolerance. | |||
These networks can be implemented even with a limited set of | These networks can be implemented even with a limited set of | |||
available quantum gates. | available quantum gates. | |||
2. Second generation quantum networks improve upon the first | 2. Second-generation quantum networks improve upon the first | |||
generation with QEC codes for error tolerance (but not loss | generation with QEC codes for error tolerance (but not loss | |||
tolerance). At first, QEC will be applied to entanglement | tolerance). At first, QEC will be applied to entanglement | |||
distillation only which requires uni-directional classical | distillation only, which requires unidirectional classical | |||
signalling. Later, QEC codes will be used to create logical Bell | signalling. Later, QEC codes will be used to create logical Bell | |||
pairs which no longer require any classical signalling for the | pairs that no longer require any classical signalling for the | |||
purposes of error tolerance. Heralding is still used to | purposes of error tolerance. Heralding is still used to | |||
compensate for transmission losses. | compensate for transmission losses. | |||
3. Third generation quantum networks directly transmit QEC encoded | 3. Third-generation quantum networks directly transmit QEC-encoded | |||
qubits to adjacent nodes, as discussed in Section 4.1.4. | qubits to adjacent nodes, as discussed in Section 4.1.4. | |||
Elementary link Bell pairs can now be created without heralding | Elementary link Bell pairs can now be created without heralding | |||
or any other classical signalling. Furthermore, this also | or any other classical signalling. Furthermore, this also | |||
enables direct transmission architectures in which qubits are | enables direct transmission architectures in which qubits are | |||
forwarded end-to-end like classical packets rather than relying | forwarded end to end like classical packets rather than relying | |||
on Bell pairs and entanglement swapping. | on Bell pairs and entanglement swapping. | |||
Despite the fact that there are important distinctions in how errors | Despite the fact that there are important distinctions in how errors | |||
will be managed in the different generations it is unlikely that all | will be managed in the different generations, it is unlikely that all | |||
quantum networks will consistently use the same method. This is due | quantum networks will consistently use the same method. This is due | |||
to different hardware requirements of the different generations and | to different hardware requirements of the different generations and | |||
the practical reality of network upgrades. Therefore, it is | the practical reality of network upgrades. Therefore, it is | |||
unavoidable that eventually boundaries between different error | unavoidable that eventually boundaries between different error | |||
management schemes start forming. This will affect the content and | management schemes start forming. This will affect the content and | |||
semantics of messages that must cross those boundaries -- both for | semantics of messages that must cross those boundaries -- for both | |||
connection setup and real-time operation [Nagayama16]. | connection setup and real-time operation [Nagayama16]. | |||
4.4.4. Delivery | 4.4.4. Delivery | |||
Eventually, the Bell pairs must be delivered to an application (or | Eventually, the Bell pairs must be delivered to an application (or | |||
higher layer protocol) at the two end-nodes. A detailed list of such | higher-layer protocol) at the two end nodes. A detailed list of such | |||
requirements is beyond the scope of this draft. At minimum, the end- | requirements is beyond the scope of this document. At minimum, the | |||
nodes require information to map a particular Bell pair to the qubit | end nodes require information to map a particular Bell pair to the | |||
in their local memory that is part of this entangled pair. | qubit in their local memory that is part of this entangled pair. | |||
5. Architecture of a quantum internet | 5. Architecture of a Quantum Internet | |||
It is evident from the previous sections that the fundamental service | It is evident from the previous sections that the fundamental service | |||
provided by a quantum network significantly differs from that of a | provided by a quantum network significantly differs from that of a | |||
classical network. Therefore, it is not surprising that the | classical network. Therefore, it is not surprising that the | |||
architecture of a quantum internet will itself be very different from | architecture of a quantum internet will itself be very different from | |||
that of the classical Internet. | that of the classical Internet. | |||
5.1. Challenges | 5.1. Challenges | |||
This subsection covers the major fundamental challenges building | This subsection covers the major fundamental challenges involved in | |||
quantum networks. Here, we only describe the fundamental | building quantum networks. Here, we only describe the fundamental | |||
differences. Technological limitations are described later. | differences. Technological limitations are described in Section 5.4. | |||
1. Bell pairs are not equivalent to payload carrying packets. | 1. Bell pairs are not equivalent to packets that carry payload. | |||
In most classical networks, including Ethernet, Internet Protocol | In most classical networks, including Ethernet, Internet Protocol | |||
(IP), and Multi-Protocol Label Switching (MPLS) networks, user | (IP), and Multi-Protocol Label Switching (MPLS) networks, user | |||
data is grouped into packets. In addition to the user data, each | data is grouped into packets. In addition to the user data, each | |||
packet also contains a series of headers which contain the | packet also contains a series of headers that contain the control | |||
control information that lets routers and switches forward it | information that lets routers and switches forward it towards its | |||
towards its destination. Packets are the fundamental unit in a | destination. Packets are the fundamental unit in a classical | |||
classical network. | network. | |||
In a quantum network, the entangled pairs of qubits are the basic | In a quantum network, the entangled pairs of qubits are the basic | |||
unit of networking. These qubits themselves do not carry any | unit of networking. These qubits themselves do not carry any | |||
headers. Therefore, quantum networks will have to send all | headers. Therefore, quantum networks will have to send all | |||
control information via separate classical channels which the | control information via separate classical channels, which the | |||
repeaters will have to correlate with the qubits stored in their | repeaters will have to correlate with the qubits stored in their | |||
memory. Furthermore, a Bell pair consists of two qubits | memory. Furthermore, unlike a classical packet, which is located | |||
distributed across two nodes which is unlike a classical packet | at a single node, a Bell pair consists of two qubits distributed | |||
which is located at a single node. This has a fundamental impact | across two nodes. This has a fundamental impact on how quantum | |||
on how quantum networks will be managed and how protocols need to | networks will be managed and how protocols need to be designed. | |||
be designed. To make long-distance Bell pairs, the nodes may | To make long-distance Bell pairs, the nodes may have to keep | |||
have to keep their qubits in their quantum memories and wait | their qubits in their quantum memories and wait until control | |||
until control information is exchanged before proceeding with the | information is exchanged before proceeding with the next | |||
next operation. This signalling will result in additional | operation. This signalling will result in additional latency, | |||
latency which will depend on the distance between the nodes | which will depend on the distance between the nodes holding the | |||
holding the two ends of the Bell pair. Error management, such as | two ends of the Bell pair. Error management, such as | |||
entanglement distillation, is a typical example of such control | entanglement distillation, is a typical example of such control | |||
information exchange [Nagayama21] (see also Section 4.4.3.3). | information exchange [Nagayama21] (see also Section 4.4.3.3). | |||
2. "Store and forward" vs "store and swap" quantum networks. | 2. "Store and forward" and "store and swap" quantum networks require | |||
different state management techniques. | ||||
As described in Section 4.4.1, quantum links provide Bell pairs | As described in Section 4.4.1, quantum links provide Bell pairs | |||
that are undirected network resources, in contrast to directed | that are undirected network resources, in contrast to directed | |||
frames of classical networks. This phenomenological distinction | frames of classical networks. This phenomenological distinction | |||
leads to architectural differences between quantum networks and | leads to architectural differences between quantum networks and | |||
classical networks. Quantum networks combine multiple elementary | classical networks. Quantum networks combine multiple elementary | |||
link Bell pairs together to create one end-to-end Bell pair, | link Bell pairs together to create one end-to-end Bell pair, | |||
whereas classical networks deliver messages from one end to the | whereas classical networks deliver messages from one end to the | |||
other end hop by hop. | other end hop by hop. | |||
Classical networks receive data on one interface, store it in | Classical networks receive data on one interface, store it in | |||
local buffers, then forward the data to another appropriate | local buffers, and then forward the data to another appropriate | |||
interface. Quantum networks store Bell pairs and then execute | interface. Quantum networks store Bell pairs and then execute | |||
entanglement swapping instead of forwarding in the data plane. | entanglement swapping instead of forwarding in the data plane. | |||
Such quantum networks are "store and swap" networks. In "store | Such quantum networks are "store and swap" networks. In "store | |||
and swap" networks, we do not need to care about the order in | and swap" networks, we do not need to care about the order in | |||
which the Bell pairs were generated since they are undirected. | which the Bell pairs were generated, since they are undirected. | |||
However, whilst the ordering does not matter, it is very | However, whilst the ordering does not matter, it is very | |||
important that the right entangled pairs get swapped, and that | important that the right entangled pairs get swapped, and that | |||
the intermediate measurement outcomes (see Section 4.4.2) are | the intermediate measurement outcomes (see Section 4.4.2) are | |||
signalled to and correlated with the correct qubits at the other | signalled to and correlated with the correct qubits at the other | |||
nodes. Otherwise, the final end-to-end entangled pair will not | nodes. Otherwise, the final end-to-end entangled pair will not | |||
be created between the expected end-points or will be in a | be created between the expected end-points or will be in a | |||
different quantum state than expected. For example, rather than | different quantum state than expected. For example, rather than | |||
Alice receiving a qubit that is entangled with Bob's qubit, her | Alice receiving a qubit that is entangled with Bob's qubit, her | |||
qubit is entangled with Charlie's qubit. This distinction makes | qubit is entangled with Charlie's qubit. This distinction makes | |||
control algorithms and optimisation of quantum networks different | control algorithms and optimisation of quantum networks different | |||
from classical ones, in the sense that swapping is stateful in | from those for classical networks, in the sense that swapping is | |||
contrast to stateless packet-by-packet forwarding. Note that | stateful in contrast to stateless packet-by-packet forwarding. | |||
third generation quantum networks, as described in Section 4.4.1, | Note that, as described in Section 4.4.3.3, third-generation | |||
will be able to support a "store and forward" architecture in | quantum networks will be able to support a "store and forward" | |||
addition to "store and swap". | architecture in addition to "store and swap". | |||
3. An entangled pair is only useful if the locations of both qubits | 3. An entangled pair is only useful if the locations of both qubits | |||
are known. | are known. | |||
A classical network packet logically exists only at one location | A classical network packet logically exists only at one location | |||
at any point in time. If a packet is modified in some way, | at any point in time. If a packet is modified in some way, | |||
whether headers or payload, this information does not need to be | whether headers or payload, this information does not need to be | |||
conveyed to anybody else in the network. The packet can be | conveyed to anybody else in the network. The packet can be | |||
simply forwarded as before. | simply forwarded as before. | |||
In contrast, entanglement is a phenomenon in which two or more | In contrast, entanglement is a phenomenon in which two or more | |||
qubits exist in a physically distributed state. Operations on | qubits exist in a physically distributed state. Operations on | |||
one of the qubits change the mutual state of the pair. Since the | one of the qubits change the mutual state of the pair. Since the | |||
owner of a particular qubit cannot just read out its state, it | owner of a particular qubit cannot just read out its state, it | |||
must coordinate all its actions with the owner of the pair's | must coordinate all its actions with the owner of the pair's | |||
other qubit. Therefore, the owner of any qubit that is part of | other qubit. Therefore, the owner of any qubit that is part of | |||
an entangled pair must know the location of its counterpart. | an entangled pair must know the location of its counterpart. | |||
Location, in this context, need not be the explicit spatial | Location, in this context, need not be the explicit spatial | |||
location. A relevant pair identifier, a means of communication | location. A relevant pair identifier, a means of communication | |||
between the pair owners, and an association between the pair ID | between the pair owners, and an association between the pair ID | |||
and the individual qubits is sufficient. | and the individual qubits will be sufficient. | |||
4. Generating entanglement requires temporary state. | 4. Generating entanglement requires temporary state. | |||
Packet forwarding in a classical network is largely a stateless | Packet forwarding in a classical network is largely a stateless | |||
operation. When a packet is received, the router does a lookup | operation. When a packet is received, the router does a lookup | |||
in its forwarding table and sends the packet out of the | in its forwarding table and sends the packet out of the | |||
appropriate output. There is no need to keep any memory of the | appropriate output. There is no need to keep any memory of the | |||
packet any more. | packet any more. | |||
A quantum node must be able to make decisions about qubits that | A quantum node must be able to make decisions about qubits that | |||
it receives and is holding in its memory. Since qubits do not | it receives and is holding in its memory. Since qubits do not | |||
carry headers, the receipt of an entangled pair conveys no | carry headers, the receipt of an entangled pair conveys no | |||
control information based on which the repeater can make a | control information based on which the repeater can make a | |||
decision. The relevant control information will arrive | decision. The relevant control information will arrive | |||
separately over a classical channel. This implies that a | separately over a classical channel. This implies that a | |||
repeater must store temporary state as the control information | repeater must store temporary state, as the control information | |||
and the qubit it pertains to will, in general, not arrive at the | and the qubit it pertains to will, in general, not arrive at the | |||
same time. | same time. | |||
5.2. Classical communication | 5.2. Classical Communication | |||
In this draft we have already covered two different roles that | In this document, we have already covered two different roles that | |||
classical communication must perform: | classical communication must perform the following: | |||
* communicate classical bits of information as part of distributed | * Communicate classical bits of information as part of distributed | |||
protocols such as entanglement swapping and teleportation, | protocols such as entanglement swapping and teleportation. | |||
* communicate control information within a network, including both | * Communicate control information within a network, including | |||
background protocols such as routing as well as signalling | background protocols such as routing, as well as signalling | |||
protocols to set up end-to-end entanglement generation. | protocols to set up end-to-end entanglement generation. | |||
Classical communication is a crucial building block of any quantum | Classical communication is a crucial building block of any quantum | |||
network. All nodes in a quantum network are assumed to have | network. All nodes in a quantum network are assumed to have | |||
classical connectivity with each other (within typical administrative | classical connectivity with each other (within typical administrative | |||
domain limits). Therefore, quantum nodes will need to manage two | domain limits). Therefore, quantum nodes will need to manage two | |||
data planes in parallel, a classical one and a quantum one. | data planes in parallel: a classical data plane and a quantum data | |||
Additionally, a node must be able to correlate information between | plane. Additionally, a node must be able to correlate information | |||
the two planes so that the control information received on a | between the two planes so that the control information received on a | |||
classical channel can be applied to the qubits managed by the quantum | classical channel can be applied to the qubits managed by the quantum | |||
data plane. | data plane. | |||
5.3. Abstract model of the network | 5.3. Abstract Model of the Network | |||
5.3.1. The control and data planes | 5.3.1. The Control Plane and the Data Plane | |||
Control plane protocols for quantum networks will have many | Control plane protocols for quantum networks will have many | |||
responsibilities similar to their classical counterparts, namely | responsibilities similar to their classical counterparts, namely | |||
discovering the network topology, resource management, populating | discovering the network topology, resource management, populating | |||
data plane tables, etc. Most of these protocols do not require the | data plane tables, etc. Most of these protocols do not require the | |||
manipulation of quantum data and can operate simply by exchanging | manipulation of quantum data and can operate simply by exchanging | |||
classical messages only. There may also be some control plane | classical messages only. There may also be some control plane | |||
functionality that does require the handling of quantum data, e.g. a | functionality that does require the handling of quantum data | |||
quantum ping [I-D.irtf-qirg-quantum-internet-use-cases]. As it is | [QI-Scenarios]. As it is not clear if there is much benefit in | |||
not clear if there is much benefit in defining a separate quantum | defining a separate quantum control plane given the significant | |||
control plane given the significant overlap in responsibilities with | overlap in responsibilities with its classical counterpart, the | |||
its classical counterpart, the question of whether there should be a | question of whether there should be a separate quantum control plane | |||
separate quantum control plane is beyond the scope of this document. | is beyond the scope of this document. | |||
However, the data plane separation is much more distinct and there | However, the data plane separation is much more distinct, and there | |||
will be two data planes: a classical data plane and a quantum data | will be two data planes: a classical data plane and a quantum data | |||
plane. The classical data plane processes and forwards classical | plane. The classical data plane processes and forwards classical | |||
packets. The quantum data plane processes and swaps entangled pairs. | packets. The quantum data plane processes and swaps entangled pairs. | |||
Third generation quantum networks may also forward qubits in addition | Third-generation quantum networks may also forward qubits in addition | |||
to swapping Bell pairs. | to swapping Bell pairs. | |||
In addition to control plane messages, there will also be control | In addition to control plane messages, there will also be control | |||
information messages that operate at the granularity of individual | information messages that operate at the granularity of individual | |||
entangled pairs, such as heralding messages used for elementary link | entangled pairs, such as heralding messages used for elementary link | |||
generation (Section 4.4.1). In terms of functionality, these | generation (Section 4.4.1). In terms of functionality, these | |||
messages are closer to classical packet headers than control plane | messages are closer to classical packet headers than control plane | |||
messages and thus we consider them to be part of the quantum data | messages, and thus we consider them to be part of the quantum data | |||
plane. Therefore, a quantum data plane also includes the exchange of | plane. Therefore, a quantum data plane also includes the exchange of | |||
classical control information at the granularity of individual qubits | classical control information at the granularity of individual qubits | |||
and entangled pairs. | and entangled pairs. | |||
5.3.2. Elements of a quantum network | 5.3.2. Elements of a Quantum Network | |||
We have identified quantum repeaters as the core building block of a | We have identified quantum repeaters as the core building block of a | |||
quantum network. However, a quantum repeater will have to do more | quantum network. However, a quantum repeater will have to do more | |||
than just entanglement swapping in a functional quantum network. Its | than just entanglement swapping in a functional quantum network. Its | |||
key responsibilities will include: | key responsibilities will include the following: | |||
1. Creating link-local entanglement between neighbouring nodes. | 1. Creating link-local entanglement between neighbouring nodes. | |||
2. Extending entanglement from link-local pairs to long-range pairs | 2. Extending entanglement from link-local pairs to long-range pairs | |||
through entanglement swapping. | through entanglement swapping. | |||
3. Performing distillation to manage the fidelity of the produced | 3. Performing distillation to manage the fidelity of the produced | |||
pairs. | pairs. | |||
4. Participating in the management of the network (routing, etc.). | 4. Participating in the management of the network (routing, etc.). | |||
Not all quantum repeaters in the network will be the same; here we | Not all quantum repeaters in the network will be the same; here, we | |||
break them down further: | break them down further: | |||
* Quantum routers (controllable quantum nodes) - A quantum router is | Quantum routers (controllable quantum nodes): A quantum router is a | |||
a quantum repeater with a control plane that participates in the | quantum repeater with a control plane that participates in the | |||
management of the network and will make decisions about which | management of the network and will make decisions about which | |||
qubits to swap to generate the requested end-to-end pairs. | qubits to swap to generate the requested end-to-end pairs. | |||
* Automated quantum nodes - An automated quantum node is a data | Automated quantum nodes: An automated quantum node is a data-plane- | |||
plane only quantum repeater that does not participate in the | only quantum repeater that does not participate in the network | |||
network control plane. Since the no-cloning theorem precludes the | control plane. Since the no-cloning theorem precludes the use of | |||
use of amplification, long-range links will be established by | amplification, long-range links will be established by chaining | |||
chaining multiple such automated nodes together. | multiple such automated nodes together. | |||
* End-nodes - End-nodes in a quantum network must be able to receive | End nodes: End nodes in a quantum network must be able to receive | |||
and handle an entangled pair, but they do not need to be able to | and handle an entangled pair, but they do not need to be able to | |||
perform an entanglement swap (and thus are not necessarily quantum | perform an entanglement swap (and thus are not necessarily quantum | |||
repeaters). End-nodes are also not required to have any quantum | repeaters). End nodes are also not required to have any quantum | |||
memory as certain quantum applications can be realised by having | memory, as certain quantum applications can be realised by having | |||
the end-node measure its qubit as soon as it is received. | the end node measure its qubit as soon as it is received. | |||
* Non-quantum nodes - Not all nodes in a quantum network need to | Non-quantum nodes: Not all nodes in a quantum network need to have a | |||
have a quantum data plane. A non-quantum node is any device that | quantum data plane. A non-quantum node is any device that can | |||
can handle classical network traffic. | handle classical network traffic. | |||
Additionally, we need to identify two kinds of links that will be | Additionally, we need to identify two kinds of links that will be | |||
used in a quantum network: | used in a quantum network: | |||
* Quantum links - A quantum link is a link which can be used to | Quantum links: A quantum link is a link that can be used to generate | |||
generate an entangled pair between two directly connected quantum | an entangled pair between two directly connected quantum | |||
repeaters. This may include additional mid-point elements | repeaters. This may include additional mid-point elements as | |||
described in Section 4.4.1. It may also include a dedicated | described in Section 4.4.1. It may also include a dedicated | |||
classical channel that is to be used solely for the purpose of | classical channel that is to be used solely for the purpose of | |||
coordinating the entanglement generation on this quantum link. | coordinating the entanglement generation on this quantum link. | |||
* Classical links - A classical link is a link between any node in | Classical links: A classical link is a link between any node in the | |||
the network that is capable of carrying classical network traffic. | network that is capable of carrying classical network traffic. | |||
Note that passive elements, such as optical switches, do not destroy | Note that passive elements, such as optical switches, do not destroy | |||
the quantum state. Therefore, it is possible to connect multiple | the quantum state. Therefore, it is possible to connect multiple | |||
quantum nodes with each other over an optical network and perform | quantum nodes with each other over an optical network and perform | |||
optical switching rather than routing via entanglement swapping at | optical switching rather than routing via entanglement swapping at | |||
quantum routers. This does require coordination with the elementary | quantum routers. This does require coordination with the elementary | |||
link entanglement generation process and it still requires repeaters | link entanglement generation process, and it still requires repeaters | |||
to overcome the short-distance limitations. However, this is a | to overcome the short-distance limitations. However, this is a | |||
potentially feasible architecture for local area networks. | potentially feasible architecture for local area networks. | |||
5.3.3. Putting it all together | 5.3.3. Putting It All Together | |||
A two-hop path in a generic quantum network can be represented as: | A two-hop path in a generic quantum network can be represented as | |||
follows: | ||||
+-----+ +-----+ | +-----+ +-----+ | |||
| App |- - - - - - - - - -CC- - - - - - - - - -| App | | | App |- - - - - - - - - -CC- - - - - - - - - -| App | | |||
+-----+ +------+ +-----+ | +-----+ +------+ +-----+ | |||
| EN |------ CL ------| QR |------ CL ------| EN | | | EN |------ CL ------| QR |------ CL ------| EN | | |||
| |------ QL ------| |------ QL ------| | | | |------ QL ------| |------ QL ------| | | |||
+-----+ +------+ +-----+ | +-----+ +------+ +-----+ | |||
App - user-level application | App - user-level application | |||
EN - end-node | EN - End Node | |||
QL - quantum link | QL - Quantum Link | |||
CL - classical link | CL - Classical Link | |||
CC - classical channel (traverses one or more CLs) | CC - Classical Channel (traverses one or more CLs) | |||
QR - quantum repeater | QR - Quantum Repeater | |||
An application (App) running on two end-nodes (ENs) attached to a | An application (App) running on two End Nodes (ENs) attached to a | |||
network will at some point need the network to generate entangled | network will at some point need the network to generate entangled | |||
pairs for its use. This may require negotiation between the end- | pairs for its use. This may require negotiation between the ENs | |||
nodes (possibly ahead of time), because they must both open a | (possibly ahead of time), because they must both open a communication | |||
communication end-point which the network can use to identify the two | end-point that the network can use to identify the two ends of the | |||
ends of the connection. The two end-nodes use a classical channel | connection. The two ENs use a Classical Channel (CC) available in | |||
(CC) available in the network to achieve this goal. | the network to achieve this goal. | |||
When the network receives a request to generate end-to-end entangled | When the network receives a request to generate end-to-end entangled | |||
pairs it uses the classical communication links (CLs) to coordinate | pairs, it uses the Classical Links (CLs) to coordinate and claim the | |||
and claim the resources necessary to fulfill this request. This may | resources necessary to fulfill this request. This may be some | |||
be some combination of prior control information (e.g. routing | combination of prior control information (e.g., routing tables) and | |||
tables) and signalling protocols, but the details of how this is | signalling protocols, but the details of how this is achieved are an | |||
achieved are an active research question. A thought experiment on | active research question. A thought experiment on what this might | |||
what this might look like be can be found later in this draft in | look like be can be found in Section 7. | |||
Section 7. | ||||
During or after the distribution of control information, the network | During or after the distribution of control information, the network | |||
performs the necessary quantum operations such as generating | performs the necessary quantum operations, such as generating | |||
entanglement over individual quantum links (QLs), performing | entanglement over individual Quantum Links (QLs), performing | |||
entanglement swaps at quantum repeaters (QRs), and further signalling | entanglement swaps at Quantum Repeaters (QRs), and further signalling | |||
to transmit the swap outcomes and other control information. Since | to transmit the swap outcomes and other control information. Since | |||
Bell pairs do not carry any user data, some of these operations can | Bell pairs do not carry any user data, some of these operations can | |||
be performed before the request is received in anticipation of the | be performed before the request is received, in anticipation of the | |||
demand. | demand. | |||
Note that here, "signalling" is used in a very broad sense and covers | Note that here, "signalling" is used in a very broad sense and covers | |||
many different types of messaging necessary for entanglement | many different types of messaging necessary for entanglement | |||
generation control. For example, heralded entanglement generation | generation control. For example, heralded entanglement generation | |||
requires very precise timing synchronisation between the neighbouring | requires very precise timing synchronisation between the neighbouring | |||
nodes and thus the triggering of entanglement generation and | nodes, and thus the triggering of entanglement generation and | |||
heralding may happen over its own, perhaps physically separate CL, as | heralding may happen over its own, perhaps physically separate, CL, | |||
was the case in network stack demonstration in [Pompili21.2]. Higher | as was the case in the network stack demonstration described in | |||
level signalling with less stringent timing requirements (e.g. | [Pompili21.2]. Higher-level signalling with timing requirements that | |||
control plane signalling) may then happen over its own CL. | are less stringent (e.g., control plane signalling) may then happen | |||
over its own CL. | ||||
The entangled pair is delivered to the application once it is ready, | The entangled pair is delivered to the application once it is ready, | |||
together with the relevant pair identifier. However, being ready | together with the relevant pair identifier. However, being ready | |||
does not necessarily mean that all link pairs and entanglement swaps | does not necessarily mean that all link pairs and entanglement swaps | |||
are complete, as some applications can start executing on an | are complete, as some applications can start executing on an | |||
incomplete pair. In this case the remaining entanglement swaps will | incomplete pair. In this case, the remaining entanglement swaps will | |||
propagate the actions across the network to the other end, sometimes | propagate the actions across the network to the other end, sometimes | |||
necessitating fixup operations at the end node. | necessitating fixup operations at the EN. | |||
5.4. Physical constraints | 5.4. Physical Constraints | |||
The model above has effectively abstracted away the particulars of | The model above has effectively abstracted away the particulars of | |||
the hardware implementation. However, certain physical constraints | the hardware implementation. However, certain physical constraints | |||
need to be considered in order to build a practical network. Some of | need to be considered in order to build a practical network. Some of | |||
these are fundamental constraints and no matter how much the | these are fundamental constraints, and no matter how much the | |||
technology improves, they will always need to be addressed. Others | technology improves, they will always need to be addressed. Others | |||
are artifacts of the early stages of a new technology. Here, we | are artifacts of the early stages of a new technology. Here, we | |||
consider a highly abstract scenario and refer to [Wehner18] for | consider a highly abstract scenario and refer to [Wehner18] for | |||
pointers to the physics literature. | pointers to the physics literature. | |||
5.4.1. Memory lifetimes | 5.4.1. Memory Lifetimes | |||
In addition to discrete operations being imperfect, storing a qubit | In addition to discrete operations being imperfect, storing a qubit | |||
in memory is also highly non-trivial. The main difficulty in | in memory is also highly non-trivial. The main difficulty in | |||
achieving persistent storage is that it is extremely challenging to | achieving persistent storage is that it is extremely challenging to | |||
isolate a quantum system from the environment. The environment | isolate a quantum system from the environment. The environment | |||
introduces an uncontrollable source of noise into the system which | introduces an uncontrollable source of noise into the system, which | |||
affects the fidelity of the state. This process is known as | affects the fidelity of the state. This process is known as | |||
decoherence. Eventually, the state has to be discarded once its | decoherence. Eventually, the state has to be discarded once its | |||
fidelity degrades too much. | fidelity degrades too much. | |||
The memory lifetime depends on the particular physical setup, but the | The memory lifetime depends on the particular physical setup, but the | |||
highest achievable values in quantum network hardware currently are | highest achievable values in quantum network hardware are, as of | |||
on the order of seconds [Abobeih18] although a lifetime of a minute | 2020, on the order of seconds [Abobeih18], although a lifetime of a | |||
has also been demonstrated for qubits not connected to a quantum | minute has also been demonstrated for qubits not connected to a | |||
network [Bradley19] (as of 2020). These values have increased | quantum network [Bradley19]. These values have increased | |||
tremendously over the lifetime of the different technologies and are | tremendously over the lifetime of the different technologies and are | |||
bound to keep increasing. However, if quantum networks are to be | bound to keep increasing. However, if quantum networks are to be | |||
realised in the near future, they need to be able to handle short | realised in the near future, they need to be able to handle short | |||
memory lifetimes, for example by reducing latency on critical paths. | memory lifetimes -- for example, by reducing latency on critical | |||
paths. | ||||
5.4.2. Rates | 5.4.2. Rates | |||
Entanglement generation on a link between two connected nodes is not | Entanglement generation on a link between two connected nodes is not | |||
a very efficient process and it requires many attempts to succeed | a very efficient process, and it requires many attempts to succeed | |||
[Hensen15] [Dahlberg19]. For example, the highest achievable rates | [Hensen15] [Dahlberg19]. For example, the highest achievable rates | |||
of success between nitrogen-vacancy center nodes, which in addition | of success between nitrogen-vacancy center nodes -- which, in | |||
to entanglement generation are also capable of storing and processing | addition to entanglement generation are also capable of storing and | |||
the resulting qubits, are on the order of 10 Hz. Combined with short | processing the resulting qubits -- are on the order of 10 Hz. | |||
memory lifetimes this leads to very tight timing windows to build up | Combined with short memory lifetimes, this leads to very tight timing | |||
network-wide connectivity. | windows to build up network-wide connectivity. | |||
Other platforms have shown higher entanglement rates, but this | Other platforms have shown higher entanglement rates, but this | |||
usually comes at the cost of other hardware capabilities, such as no | usually comes at the cost of other hardware capabilities, such as no | |||
quantum memory and/or limited processing capabilities [Wei22]. | quantum memory and/or limited processing capabilities [Wei22]. | |||
Nevertheless, the current rates are not sufficient for practical | Nevertheless, the current rates are not sufficient for practical | |||
applications beyond simple experimental proofs of concept. However, | applications beyond simple experimental proofs of concept. However, | |||
they are expected to improve over time as quantum network technology | they are expected to improve over time as quantum network technology | |||
evolves [Wei22]. | evolves [Wei22]. | |||
5.4.3. Communication qubits | 5.4.3. Communication Qubits | |||
Most physical architectures capable of storing qubits are only able | Most physical architectures capable of storing qubits are only able | |||
to generate entanglement using only a subset of available qubits | to generate entanglement using only a subset of available qubits | |||
called communication qubits [Dahlberg19]. Once a Bell pair has been | called communication qubits [Dahlberg19]. Once a Bell pair has been | |||
generated using a communication qubit, its state can be transferred | generated using a communication qubit, its state can be transferred | |||
into memory. This may impose additional limitations on the network. | into memory. This may impose additional limitations on the network. | |||
In particular, if a given node has only one communication qubit it | In particular, if a given node has only one communication qubit, it | |||
cannot simultaneously generate Bell pairs over two links. It must | cannot simultaneously generate Bell pairs over two links. It must | |||
generate entanglement over the links one at a time. | generate entanglement over the links one at a time. | |||
5.4.4. Homogeneity | 5.4.4. Homogeneity | |||
Currently all existing quantum network implementations are | At present, all existing quantum network implementations are | |||
homogeneous and they do not interface with each other. In general, | homogeneous, and they do not interface with each other. In general, | |||
it is very challenging to combine different quantum information | it is very challenging to combine different quantum information | |||
processing technologies. | processing technologies. | |||
There are many different physical hardware platforms for implementing | There are many different physical hardware platforms for implementing | |||
quantum networking hardware. The different technologies differ in | quantum networking hardware. The different technologies differ in | |||
how they store and manipulate qubits in memory and how they generate | how they store and manipulate qubits in memory and how they generate | |||
entanglement across a link with their neighbours. For example, | entanglement across a link with their neighbours. For example, | |||
hardware based on optical elements and atomic ensembles [Sangouard11] | hardware based on optical elements and atomic ensembles [Sangouard11] | |||
is very efficient at generating entanglement at high rates, but | is very efficient at generating entanglement at high rates but | |||
provides limited processing capabilities once the entanglement is | provides limited processing capabilities once the entanglement is | |||
generated. On the other hand, nitrogen-vacancy based [Hensen15] or | generated. On the other hand, nitrogen-vacancy-based platforms | |||
trapped ion [Moehring07] platforms offer a much greater degree of | [Hensen15] or trapped ion platforms [Moehring07] offer a much greater | |||
control over the qubits, but have a harder time generating | degree of control over the qubits but have a harder time generating | |||
entanglement at high rates. | entanglement at high rates. | |||
In order to overcome the weaknesses of the different platforms, | In order to overcome the weaknesses of the different platforms, | |||
coupling the different technologies will help to build fully | coupling the different technologies will help to build fully | |||
functional networks. For example, end-nodes may be implemented using | functional networks. For example, end nodes may be implemented using | |||
technology with good qubit processing capabilities to enable complex | technology with good qubit processing capabilities to enable complex | |||
applications, but automated quantum nodes that that serve only to | applications, but automated quantum nodes that serve only to "repeat" | |||
"repeat" along a linear chain, where the processing logic is much | along a linear chain, where the processing logic is much simpler, can | |||
simpler, can be implemented with technologies that sacrifice | be implemented with technologies that sacrifice processing | |||
processing capabilities for higher entanglement rates at long | capabilities for higher entanglement rates at long distances | |||
distances [Askarani21]. | [Askarani21]. | |||
This point is further exacerbated by the fact that quantum computers | This point is further exacerbated by the fact that quantum computers | |||
(i.e. end-nodes in a quantum network) are often based on different | (i.e., end nodes in a quantum network) are often based on different | |||
hardware platforms than quantum repeaters thus requiring a coupling | hardware platforms than quantum repeaters, thus requiring a coupling | |||
(transduction) between the two. This is especially true for quantum | (transduction) between the two. This is especially true for quantum | |||
computers based on superconducting technology which are challenging | computers based on superconducting technology, which are challenging | |||
to connect to optical networks. However, even trapped ion quantum | to connect to optical networks. However, even trapped ion quantum | |||
computers, which is a platform that has shown promise for quantum | computers, which make up a platform that has shown promise for | |||
networking, will still need to connect to other platforms that are | quantum networking, will still need to connect to other platforms | |||
better at creating entanglement at high rates over long distances | that are better at creating entanglement at high rates over long | |||
(hundreds of kms). | distances (hundreds of kilometres). | |||
6. Architectural principles | 6. Architectural Principles | |||
Given that the most practical way of realising quantum network | Given that the most practical way of realising quantum network | |||
connectivity is using Bell pair and entanglement swapping repeater | connectivity is using Bell pair and entanglement-swapping repeater | |||
technology, what sort of principles should guide us in assembling | technology, what sort of principles should guide us in assembling | |||
such networks such that they are functional, robust, efficient, and | such networks such that they are functional, robust, efficient, and, | |||
most importantly, do they work? Furthermore, how do we design | most importantly, will work? Furthermore, how do we design networks | |||
networks so that they work under the constraints imposed by the | so that they work under the constraints imposed by the hardware | |||
hardware available today, but do not impose unnecessary burdens on | available today but do not impose unnecessary burdens on future | |||
future technology? | technology? | |||
As quantum networking is a completely new technology that is likely | As quantum networking is a completely new technology that is likely | |||
to see many iterations over its lifetime, this draft must not serve | to see many iterations over its lifetime, this document must not | |||
as a definitive set of rules, but merely as a general set of | serve as a definitive set of rules but merely as a general set of | |||
recommended guidelines for the first generations of quantum networks | recommended guidelines for the first generations of quantum networks | |||
based on principles and observations made by the community. The | based on principles and observations made by the community. The | |||
benefit of having a community built document at this early stage is | benefit of having a community-built document at this early stage is | |||
that expertise in both quantum information and network architecture | that expertise in both quantum information and network architecture | |||
is needed in order to successfully build a quantum internet. | is needed in order to successfully build a quantum internet. | |||
6.1. Goals of a quantum internet | 6.1. Goals of a Quantum Internet | |||
When outlining any set of principles we must ask ourselves what goals | When outlining any set of principles, we must ask ourselves what | |||
do we want to achieve as inevitably trade-offs must be made. So what | goals we want to achieve, as inevitably trade-offs must be made. So, | |||
sort of goals should drive a quantum network architecture? The | what sort of goals should drive a quantum network architecture? The | |||
following list has been inspired by the history of computer | following list has been inspired by the history of computer | |||
networking and thus it is inevitably very similar to one that could | networking, and thus it is inevitably very similar to one that could | |||
be produced for the classical Internet [Clark88]. However, whilst | be produced for the classical Internet [Clark88]. However, whilst | |||
the goals may be similar the challenges involved are often | the goals may be similar, the challenges involved are often | |||
fundamentally different. The list will also most likely evolve with | fundamentally different. The list will also most likely evolve with | |||
time and the needs of its users. | time and the needs of its users. | |||
1. Support distributed quantum applications | 1. Support distributed quantum applications. | |||
This goal seems trivially obvious, but makes a subtle, but | This goal seems trivially obvious, but it makes a subtle, but | |||
important point which highlights a key difference between quantum | important, point that highlights a key difference between quantum | |||
and classical networks. Ultimately, quantum data transmission is | and classical networks. Ultimately, quantum data transmission is | |||
not the goal of a quantum network - it is only one possible | not the goal of a quantum network -- it is only one possible | |||
component of more advanced quantum application protocols | component of quantum application protocols that are more advanced | |||
[Wehner18]. Whilst transmission certainly could be used as a | [Wehner18]. Whilst transmission certainly could be used as a | |||
building block for all quantum applications, it is not the most | building block for all quantum applications, it is not the most | |||
basic one possible. For example, entanglement-based QKD, the | basic one possible. For example, entanglement-based QKD, the | |||
most well known quantum application protocol, only relies on the | most well-known quantum application protocol, only relies on the | |||
stronger-than-classical correlations and inherent secrecy of | stronger-than-classical correlations and inherent secrecy of | |||
entangled Bell pairs and does not have to transmit arbitrary | entangled Bell pairs and does not have to transmit arbitrary | |||
quantum states [Ekert91]. | quantum states [Ekert91]. | |||
The primary purpose of a quantum internet is to support | The primary purpose of a quantum internet is to support | |||
distributed quantum application protocols and it is of utmost | distributed quantum application protocols, and it is of utmost | |||
importance that they can run well and efficiently. Thus, it is | importance that they can run well and efficiently. Thus, it is | |||
important to develop performance metrics meaningful to | important to develop performance metrics meaningful to | |||
application to drive the development of quantum network | applications to drive the development of quantum network | |||
protocols. For example, the Bell pair generation rate is | protocols. For example, the Bell pair generation rate is | |||
meaningless if one does not also consider their fidelity. It is | meaningless if one does not also consider their fidelity. It is | |||
generally much easier to generate pairs of lower fidelity, but | generally much easier to generate pairs of lower fidelity, but | |||
quantum applications may have to make multiple re-attempts or | quantum applications may have to make multiple reattempts or even | |||
even abort if the fidelity is too low. A review of the | abort if the fidelity is too low. A review of the requirements | |||
requirements for different known quantum applications can be | for different known quantum applications can be found in | |||
found in [Wehner18] and an overview of use-cases can be found in | [Wehner18], and an overview of use cases can be found in | |||
[I-D.irtf-qirg-quantum-internet-use-cases]. | [QI-Scenarios]. | |||
2. Support tomorrow's distributed quantum applications | 2. Support tomorrow's distributed quantum applications. | |||
The only principle of the Internet that should survive | The only principle of the Internet that should survive | |||
indefinitely is the principle of constant change [RFC1958]. | indefinitely is the principle of constant change [RFC1958]. | |||
Technical change is continuous and the size and capabilities of | Technical change is continuous, and the size and capabilities of | |||
the quantum internet will change by orders of magnitude. | the quantum internet will change by orders of magnitude. | |||
Therefore, it is an explicit goal that a quantum internet | Therefore, it is an explicit goal that a quantum internet | |||
architecture be able to embrace this change. We have the benefit | architecture be able to embrace this change. We have the benefit | |||
of having been witness to the evolution of the classical Internet | of having been witness to the evolution of the classical Internet | |||
over several decades and seen what worked and what did not. It | over several decades, and we have seen what worked and what did | |||
is vital for a quantum internet to avoid the need for flag days | not. It is vital for a quantum internet to avoid the need for | |||
(e.g. NCP to TCP/IP) or upgrades that take decades to roll out | flag days (e.g., NCP to TCP/IP) or upgrades that take decades to | |||
(e.g. IPv4 to IPv6). | roll out (e.g., IPv4 to IPv6). | |||
Therefore, it is important that any proposed architecture for | Therefore, it is important that any proposed architecture for | |||
general purpose quantum repeater networks can integrate new | general-purpose quantum repeater networks can integrate new | |||
devices and solutions as they become available. The architecture | devices and solutions as they become available. The architecture | |||
should not be constrained due to considerations for early-stage | should not be constrained due to considerations for early-stage | |||
hardware and applications. For example, it is already possible | hardware and applications. For example, it is already possible | |||
to run QKD efficiently on metropolitan scales and such networks | to run QKD efficiently on metropolitan-scale networks, and such | |||
are already commercially available. However, they are not based | networks are already commercially available. However, they are | |||
on quantum repeaters and thus will not be able to easily | not based on quantum repeaters and thus will not be able to | |||
transition to more sophisticated applications. | easily transition to applications that are more sophisticated. | |||
3. Support heterogeneity | 3. Support heterogeneity. | |||
There are multiple proposals for realising practical quantum | There are multiple proposals for realising practical quantum | |||
repeater hardware and they all have their advantages and | repeater hardware, and they all have their advantages and | |||
disadvantages. Some may offer higher Bell pair generation rates | disadvantages. Some may offer higher Bell pair generation rates | |||
on individual links at the cost of more difficult entanglement | on individual links at the cost of entanglement swap operations | |||
swap operations. Other platforms may be good all around, but are | that are more difficult. Other platforms may be good all around | |||
more difficult to build. | but are more difficult to build. | |||
In addition to physical boundaries, there may be distinctions in | In addition to physical boundaries, there may be distinctions in | |||
how errors are managed (Section 4.4.3.3). These difference will | how errors are managed (Section 4.4.3.3). These differences will | |||
affect the content and semantics of messages that cross these | affect the content and semantics of messages that cross these | |||
boundaries -- both for connection setup and real-time operation. | boundaries -- for both connection setup and real-time operation. | |||
The optimal network configuration will likely leverage the | The optimal network configuration will likely leverage the | |||
advantages of multiple platforms to optimise the provided | advantages of multiple platforms to optimise the provided | |||
service. Therefore, it is an explicit goal to incorporate varied | service. Therefore, it is an explicit goal to incorporate varied | |||
hardware and technology support from the beginning. | hardware and technology support from the beginning. | |||
4. Ensure security at the network level | 4. Ensure security at the network level. | |||
The question of security in quantum networks is just as critical | The question of security in quantum networks is just as critical | |||
as it is in the classical Internet, especially since enhanced | as it is in the classical Internet, especially since enhanced | |||
security offered by quantum entanglement is one of the key | security offered by quantum entanglement is one of the key | |||
driving factors. | driving factors. | |||
Fortunately, from an application's point of view, as long as the | Fortunately, from an application's point of view, as long as the | |||
underlying implementation corresponds to (or sufficiently | underlying implementation corresponds to (or sufficiently | |||
approximates) theoretical models of quantum cryptography, quantum | approximates) theoretical models of quantum cryptography, quantum | |||
cryptographic protocols do not need the network to provide any | cryptographic protocols do not need the network to provide any | |||
guarantees about the confidentiality or integrity of the | guarantees about the confidentiality or integrity of the | |||
transmitted qubits or the generated entanglement (though they may | transmitted qubits or the generated entanglement (though they may | |||
impose requirements on the classical channel, e.g to be | impose requirements on the classical channel, e.g., to be | |||
authenticated [Wang21]). Instead, applications will leverage the | authenticated [Wang21]). Instead, applications will leverage the | |||
classical networks to establish the end-to-end security of the | classical networks to establish the end-to-end security of the | |||
results obtained from the processing of entangled qubits. | results obtained from the processing of entangled qubits. | |||
However, it is important to note that whilst classical networks | However, it is important to note that whilst classical networks | |||
are necessary to establish these end-to-end guarantees, the | are necessary to establish these end-to-end guarantees, the | |||
security relies on the properties of quantum entanglement. For | security relies on the properties of quantum entanglement. For | |||
example, QKD uses classical information reconciliation [Tang19] | example, QKD uses classical information reconciliation [Tang19] | |||
for error correction and privacy amplification [Elkouss11] for | for error correction and privacy amplification [Elkouss11] for | |||
generating the final secure key, but the raw bits that are fed | generating the final secure key, but the raw bits that are fed | |||
into these protocols must come from measuring entangled qubits | into these protocols must come from measuring entangled qubits | |||
[Ekert91]. In another application, secure delegated quantum | [Ekert91]. In another application, secure delegated quantum | |||
computing, the client hides its computation from the server by | computing, the client hides its computation from the server by | |||
sending qubits to the server and then requesting it (in a | sending qubits to the server and then requesting (in a classical | |||
classical message) to measure them in an encoded basis. The | message) that the server measure them in an encoded basis. The | |||
client then decodes the results it receives from the server to | client then decodes the results it receives from the server to | |||
obtain the result of the computation [Broadbent10]. Once again, | obtain the result of the computation [Broadbent10]. Once again, | |||
whilst a classical network is used to achieve the goal of secure | whilst a classical network is used to achieve the goal of secure | |||
computation, the remote computation is strictly quantum. | computation, the remote computation is strictly quantum. | |||
Nevertheless, whilst applications can ensure their own end-to-end | Nevertheless, whilst applications can ensure their own end-to-end | |||
security, network protocols themselves should be security aware | security, network protocols themselves should be security aware | |||
in order to protect the network itself and limit disruption. | in order to protect the network itself and limit disruption. | |||
Whilst the applications remain secure they are not necessarily | Whilst the applications remain secure, they are not necessarily | |||
operational or as efficient in the presence of an attacker. For | operational or as efficient in the presence of an attacker. For | |||
example, if an attacker can measure every qubit between two | example, if an attacker can measure every qubit between two | |||
parties trying to establish a key using QKD, no secret key can be | parties trying to establish a key using QKD, no secret key can be | |||
generated. Security concerns in quantum networks are described | generated. Security concerns in quantum networks are described | |||
in more detail in [Satoh17] [Satoh20]. | in more detail in [Satoh17] and [Satoh20]. | |||
5. Make them easy to monitor | 5. Make them easy to monitor. | |||
In order to manage, evaluate the performance of, or debug a | In order to manage, evaluate the performance of, or debug a | |||
network it is necessary to have the ability to monitor the | network, it is necessary to have the ability to monitor the | |||
network while ensuring there will be mechanisms in place to | network while ensuring that there will be mechanisms in place to | |||
protect the confidentiality and integrity of the devices | protect the confidentiality and integrity of the devices | |||
connected to it. Quantum networks bring new challenges in this | connected to it. Quantum networks bring new challenges in this | |||
area so it should be a goal of a quantum network architecture to | area, so it should be a goal of a quantum network architecture to | |||
make this task easy. | make this task easy. | |||
The fundamental unit of quantum information, the qubit, cannot be | The fundamental unit of quantum information, the qubit, cannot be | |||
actively monitored as any readout irreversibly destroys its | actively monitored, as any readout irreversibly destroys its | |||
contents. One of the implications of this fact is that measuring | contents. One of the implications of this fact is that measuring | |||
an individual pair's fidelity is impossible. Fidelity is | an individual pair's fidelity is impossible. Fidelity is | |||
meaningful only as a statistical quantity which requires the | meaningful only as a statistical quantity that requires constant | |||
constant monitoring and the sacrifice of generated Bell pairs for | monitoring of generated Bell pairs, achieved by sacrificing some | |||
tomography or other methods. | Bell pairs for use in tomography or other methods. | |||
Furthermore, given one end of an entangled pair, it is impossible | Furthermore, given one end of an entangled pair, it is impossible | |||
to tell where the other qubit is without any additional classical | to tell where the other qubit is without any additional classical | |||
metadata. It is impossible to extract this information from the | metadata. It is impossible to extract this information from the | |||
qubits themselves. This implies that tracking entangled pairs | qubits themselves. This implies that tracking entangled pairs | |||
necessitates some exchange of classical information. This | necessitates some exchange of classical information. This | |||
information might include (i) a reference to the entangled pair | information might include (i) a reference to the entangled pair | |||
that allows distributed applications to coordinate actions on | that allows distributed applications to coordinate actions on | |||
qubits of the same pair, and (ii) the two bits from each | qubits of the same pair and (ii) the two bits from each | |||
entanglement swap necessary to identify the final state of the | entanglement swap necessary to identify the final state of the | |||
Bell pair (Section 4.4.2). | Bell pair (Section 4.4.2). | |||
6. Ensure availability and resilience | 6. Ensure availability and resilience. | |||
Any practical and usable network, classical or quantum, must be | Any practical and usable network, classical or quantum, must be | |||
able to continue to operate despite losses and failures, and be | able to continue to operate despite losses and failures and be | |||
robust to malicious actors trying to disable connectivity. What | robust to malicious actors trying to disable connectivity. A | |||
differs in quantum networks as compared to classical networks in | difference between quantum and classical networks is that quantum | |||
this regard is that we now have two data planes and two types of | networks are composed of two types of data planes (quantum and | |||
channels to worry about: a quantum and a classical one. | classical) and two types of channels (quantum and classical) that | |||
Therefore, availability and resilience will most likely require a | must be considered. Therefore, availability and resilience will | |||
more advanced treatment than they do in classical networks. | most likely require a more advanced treatment than they do in | |||
classical networks. | ||||
Note that privacy, whilst related to security, is not listed as an | Note that privacy, whilst related to security, is not listed as an | |||
explicit goal, because the privacy benefits will depend on the use | explicit goal, because the privacy benefits will depend on the use | |||
case. For example, QKD only provides increased security for the | case. For example, QKD only provides increased security for the | |||
distribution of symmetric keys [Bennett14] [Ekert91]. The handling, | distribution of symmetric keys [Bennett14] [Ekert91]. The handling, | |||
manipulation, sharing, encryption, and decryption of data will remain | manipulation, sharing, encryption, and decryption of data will remain | |||
entirely classical limiting the benefits to privacy that can be | entirely classical, limiting the benefits to privacy that can be | |||
gained from using a quantum network. On the other hand, there are | gained from using a quantum network. On the other hand, there are | |||
applications like blind quantum computation which provides the user | applications like blind quantum computation, which provides the user | |||
with the ability to execute a quantum computation on a remote server | with the ability to execute a quantum computation on a remote server | |||
without the server knowing what the computation was or its input and | without the server knowing what the computation was or its input and | |||
output [Fitzsimons17]. Therefore, privacy must be considered on a | output [Fitzsimons17]. Therefore, privacy must be considered on a | |||
per-application basis. An overview of quantum network use cases can | per-application basis. An overview of quantum network use cases can | |||
be found in [I-D.irtf-qirg-quantum-internet-use-cases]. | be found in [QI-Scenarios]. | |||
6.2. The principles of a quantum internet | 6.2. The Principles of a Quantum Internet | |||
The principles support the goals, but are not goals themselves. The | The principles support the goals but are not goals themselves. The | |||
goals define what we want to build and the principles provide a | goals define what we want to build, and the principles provide a | |||
guideline in how we might achieve this. The goals will also be the | guideline for how we might achieve this. The goals will also be the | |||
foundation for defining any metric of success for a network | foundation for defining any metric of success for a network | |||
architecture, whereas the principles in themselves do not distinguish | architecture, whereas the principles in themselves do not distinguish | |||
between success and failure. For more information about design | between success and failure. For more information about design | |||
considerations for quantum networks see [VanMeter13.1] [Dahlberg19]. | considerations for quantum networks, see [VanMeter13.1] and | |||
[Dahlberg19]. | ||||
1. Entanglement is the fundamental service | 1. Entanglement is the fundamental service. | |||
The key service that a quantum network provides is the | The key service that a quantum network provides is the | |||
distribution of entanglement between the nodes in a network. All | distribution of entanglement between the nodes in a network. All | |||
distributed quantum applications are built on top of this key | distributed quantum applications are built on top of this key | |||
resource. Applications such as clustered quantum computing, | resource. Applications such as clustered quantum computing, | |||
distributed quantum computing, distributed quantum sensing | distributed quantum computing, distributed quantum sensing | |||
networks, and certain kinds of quantum secure networks all | networks, and certain kinds of quantum secure networks all | |||
consume quantum entanglement as a resource. Some applications | consume quantum entanglement as a resource. Some applications | |||
(e.g. quantum key distribution) simply measure the entangled | (e.g., QKD) simply measure the entangled qubits to obtain a | |||
qubits to obtain a shared secret key [QKD]. Other applications | shared secret key [QKD]. Other applications (e.g., distributed | |||
(e.g. distributed quantum computing) build more complex | quantum computing) build abstractions and operations that are | |||
abstractions and operations on the entangled qubits, e.g., | more complex on the entangled qubits, e.g., distributed CNOT | |||
distributed CNOT gates [DistCNOT] or teleportation of arbitrary | gates [DistCNOT] or teleportation of arbitrary qubit states | |||
qubit states [Teleportation]. | [Teleportation]. | |||
A quantum network may also distribute multipartite entangled | A quantum network may also distribute multipartite entangled | |||
states (entangled states of three or more qubits) [Meignant19] | states (entangled states of three or more qubits) [Meignant19], | |||
which are useful for applications such as conference key | which are useful for applications such as conference key | |||
agreement [Murta20], distributed quantum computing [Cirac99], | agreement [Murta20], distributed quantum computing [Cirac99], | |||
secret sharing [Qin17], and clock synchronisation [Komar14]. | secret sharing [Qin17], and clock synchronisation [Komar14], | |||
Though it was worth noting that multipartite entangled states can | though it is worth noting that multipartite entangled states can | |||
also be constructed from multiple entangled pairs distributed | also be constructed from multiple entangled pairs distributed | |||
between the end-nodes. | between the end nodes. | |||
2. Bell Pairs are indistinguishable | 2. Bell pairs are indistinguishable. | |||
Any two Bell Pairs between the same two nodes are | Any two Bell pairs between the same two nodes are | |||
indistinguishable for the purposes of an application provided | indistinguishable for the purposes of an application, provided | |||
they both satisfy its required fidelity threshold. This | they both satisfy its required fidelity threshold. This | |||
observation is likely to be key in enabling a more optimal | observation is likely to be key in enabling a more optimal | |||
allocation of resources in a network, e.g. for the purposes of | allocation of resources in a network, e.g., for the purposes of | |||
provisioning resources to meet application demand. However, the | provisioning resources to meet application demand. However, the | |||
qubits that make up the pair themselves are not indistinguishable | qubits that make up the pair themselves are not | |||
and the two nodes operating on a pair must coordinate to make | indistinguishable, and the two nodes operating on a pair must | |||
sure they are operating on qubits that belong to the same Bell | coordinate to make sure they are operating on qubits that belong | |||
pair. | to the same Bell pair. | |||
3. Fidelity is part of the service | 3. Fidelity is part of the service. | |||
In addition to being able to deliver Bell pairs to the | In addition to being able to deliver Bell pairs to the | |||
communication end-points, the Bell Pairs must be of sufficient | communication end-points, the Bell pairs must be of sufficient | |||
fidelity. Unlike in classical networks where most errors are | fidelity. Unlike in classical networks, where most errors are | |||
effectively eliminated before reaching the application, many | effectively eliminated before reaching the application, many | |||
quantum applications only need imperfect entanglement to | quantum applications only need imperfect entanglement to | |||
function. However, quantum applications will generally have a | function. However, quantum applications will generally have a | |||
threshold for Bell pair fidelity below which they are no longer | threshold for Bell pair fidelity below which they are no longer | |||
able to operate. Different applications will have different | able to operate. Different applications will have different | |||
requirements for what fidelity they can work with. It is the | requirements for what fidelity they can work with. It is the | |||
network's responsibility to balance the resource usage with | network's responsibility to balance the resource usage with | |||
respect to the applications' requirements. It may be that it is | respect to the applications' requirements. It may be that it is | |||
cheaper for the network to provide lower fidelity pairs that are | cheaper for the network to provide lower-fidelity pairs that are | |||
just above the threshold required by the application than it is | just above the threshold required by the application than it is | |||
to guarantee high fidelity pairs to all applications regardless | to guarantee high-fidelity pairs to all applications regardless | |||
of their requirements. | of their requirements. | |||
4. Time is an expensive resource | 4. Time is an expensive resource. | |||
Time is not the only resource that is in short supply (memory, | Time is not the only resource that is in short supply | |||
and communication qubits are as well), but ultimately it is the | (communication qubits and memory are as well), but ultimately it | |||
lifetime of quantum memories that imposes some of the most | is the lifetime of quantum memories that imposes some of the most | |||
difficult conditions for operating an extended network of quantum | difficult conditions for operating an extended network of quantum | |||
nodes. Current hardware has low rates of Bell pair generation, | nodes. Current hardware has low rates of Bell pair generation, | |||
short memory lifetimes, and access to a limited number of | short memory lifetimes, and access to a limited number of | |||
communication qubits. All these factors combined mean that even | communication qubits. All these factors combined mean that even | |||
a short waiting queue at some node could be enough for a Bell | a short waiting queue at some node could be enough for a Bell | |||
pair to decohere or result in an end-to-end pair below an | pair to decohere or result in an end-to-end pair below an | |||
application's fidelity threshold. Therefore, managing the idle | application's fidelity threshold. Therefore, managing the idle | |||
time of qubits holding live quantum states should be done | time of qubits holding live quantum states should be done | |||
carefully. Ideally by minimising the idle time, but potentially | carefully -- ideally by minimising the idle time, but potentially | |||
also by moving the quantum state for temporary storage to a | also by moving the quantum state for temporary storage to a | |||
quantum memory with a longer lifetime. | quantum memory with a longer lifetime. | |||
5. Be flexible with regards to capabilities and limitations | 5. Be flexible with regards to capabilities and limitations. | |||
This goal encompasses two important points. First, the | This goal encompasses two important points: | |||
architecture should be able to function under the physical | ||||
constraints imposed by the current generation hardware. Near- | ||||
future hardware will have low entanglement generation rates, | ||||
quantum memories able to hold a handful of qubits at best, and | ||||
decoherence rates that will render many generated pairs unusable. | ||||
Second, the architecture should not make it difficult to run the | * First, the architecture should be able to function under the | |||
network over any hardware that may come along in the future. The | physical constraints imposed by the current-generation | |||
physical capabilities of repeaters will improve and redeploying a | hardware. Near-future hardware will have low entanglement | |||
technology is extremely challenging. | generation rates, quantum memories able to hold a handful of | |||
qubits at best, and decoherence rates that will render many | ||||
generated pairs unusable. | ||||
7. A thought experiment inspired by classical networks | * Second, the architecture should not make it difficult to run | |||
the network over any hardware that may come along in the | ||||
future. The physical capabilities of repeaters will improve, | ||||
and redeploying a technology is extremely challenging. | ||||
7. A Thought Experiment Inspired by Classical Networks | ||||
To conclude, we discuss a plausible quantum network architecture | To conclude, we discuss a plausible quantum network architecture | |||
inspired by MPLS. This is not an architecture proposal, but rather a | inspired by MPLS. This is not an architecture proposal but rather a | |||
thought experiment to give the reader an idea of what components are | thought experiment to give the reader an idea of what components are | |||
necessary for a functional quantum network. We use classical MPLS as | necessary for a functional quantum network. We use classical MPLS as | |||
a basis as it is well known and understood in the networking | a basis, as it is well known and understood in the networking | |||
community. | community. | |||
Creating end-to-end Bell pairs between remote end-points is a | Creating end-to-end Bell pairs between remote end-points is a | |||
stateful distributed task that requires a lot of a-priori | stateful distributed task that requires a lot of a priori | |||
coordination. Therefore, a connection-oriented approach seems the | coordination. Therefore, a connection-oriented approach seems the | |||
most natural for quantum networks. In connection-oriented quantum | most natural for quantum networks. In connection-oriented quantum | |||
networks, when two quantum application end-points wish to start | networks, when two quantum application end-points wish to start | |||
creating end-to-end Bell pairs, they must first create a quantum | creating end-to-end Bell pairs, they must first create a Quantum | |||
virtual circuit (QVC). As an analogy, in MPLS networks end-points | Virtual Circuit (QVC). As an analogy, in MPLS networks, end-points | |||
must establish a label switched path (LSP) before exchanging traffic. | must establish a Label Switched Path (LSP) before exchanging traffic. | |||
Connection-oriented quantum networks may also support virtual | Connection-oriented quantum networks may also support virtual | |||
circuits with multiple end-points for creating multipartite | circuits with multiple end-points for creating multipartite | |||
entanglement. As an analogy, MPLS networks have the concept of | entanglement. As an analogy, MPLS networks have the concept of | |||
multi-point LSPs for multicast. | multipoint LSPs for multicast. | |||
When a quantum application creates a quantum virtual circuit, it can | When a quantum application creates a QVC, it can indicate Quality of | |||
indicate quality of service (QoS) parameters such as the required | Service (QoS) parameters such as the required capacity in end-to-end | |||
capacity in end-to-end Bell pairs per second (BPPS) and the required | Bell Pairs Per Second (BPPS) and the required fidelity of the Bell | |||
fidelity of the Bell pairs. As an analogy, in MPLS networks | pairs. As an analogy, in MPLS networks, applications specify the | |||
applications specify the required bandwidth in bits per second (BPS) | required bandwidth in Bits Per Second (BPS) and other constraints | |||
and other constraints when they create a new LSP. | when they create a new LSP. | |||
Different applications will have different QoS requirements. For | Different applications will have different QoS requirements. For | |||
example, applications such as QKD, that don't need to process the | example, applications such as QKD that don't need to process the | |||
entangled qubits and only need measure them and store the resulting | entangled qubits, and only need measure them and store the resulting | |||
outcome, may require a large volume of entanglement, but will be | outcome, may require a large volume of entanglement but will be | |||
tolerant of delay and jitter for individual pairs. On the other | tolerant of delay and jitter for individual pairs. On the other | |||
hand, distributed/cloud quantum computing applications may need fewer | hand, distributed/cloud quantum computing applications may need fewer | |||
entangled pairs, but instead, may need all of them to be generated in | entangled pairs but instead may need all of them to be generated in | |||
one go so that they can be processed all together before any of them | one go so that they can all be processed together before any of them | |||
decohere. | decohere. | |||
Quantum networks need a routing function to compute the optimal path | Quantum networks need a routing function to compute the optimal path | |||
(i.e. the best sequence of routers and links) for each new quantum | (i.e., the best sequence of routers and links) for each new QVC. The | |||
virtual circuit. The routing function may be centralized or | routing function may be centralised or distributed. In the latter | |||
distributed. In the latter case, the quantum network needs a | case, the quantum network needs a distributed routing protocol. As | |||
distributed routing protocol. As an analogy, classical networks use | an analogy, classical networks use routing protocols such as Open | |||
routing protocols such as open shortest path first (OSPF) and | Shortest Path First (OSPF) and Intermediate System to Intermediate | |||
intermediate-system to intermediate system (IS-IS). However, note | System (IS-IS). However, note that the definition of "shortest path" | |||
that the definition of "shortest-path"/"least-cost" may be different | / "least cost" may be different in a quantum network to account for | |||
in a quantum network to account for its non-classical features, such | its non-classical features, such as fidelity [VanMeter13.2]. | |||
as fidelity [VanMeter13.2]. | ||||
Given the very scarce availability of resources in early quantum | Given the very scarce availability of resources in early quantum | |||
networks, a traffic engineering function is likely to be beneficial. | networks, a Traffic Engineering (TE) function is likely to be | |||
Without traffic engineering, quantum virtual circuits always use the | beneficial. Without TE, QVCs always use the shortest path. In this | |||
shortest path. In this case, the quantum network cannot guarantee | case, the quantum network cannot guarantee that each quantum end- | |||
that each quantum end-point will get its Bell pairs at the required | point will get its Bell pairs at the required rate or fidelity. This | |||
rate or fidelity. This is analogous to "best effort" service in | is analogous to "best effort" service in classical networks. | |||
classical networks. | ||||
With traffic engineering, quantum virtual circuits choose a path that | With TE, QVCs choose a path that is guaranteed to have the requested | |||
is guaranteed to have the requested resources (e.g. bandwidth in | resources (e.g., bandwidth in BPPS) available, taking into account | |||
BPPS) available, taking into account the capacity of the routers and | the capacity of the routers and links and also taking into account | |||
links and taking into account the resources already consumed by other | the resources already consumed by other virtual circuits. As an | |||
virtual circuits. As an analogy, both OSPF and IS-IS have traffic | analogy, both OSPF and IS-IS have TE extensions to keep track of used | |||
engineering (TE) extensions to keep track of used and available | and available resources and can use Constrained Shortest Path First | |||
resources, and can use constrained shortest path first (CSPF) to take | (CSPF) to take resource availability and other constraints into | |||
resource availability and other constraints into account when | account when computing the optimal path. | |||
computing the optimal path. | ||||
The use of traffic engineering implies the use of call admission | The use of TE implies the use of Call Admission Control (CAC): the | |||
control (CAC): the network denies any virtual circuits for which it | network denies any virtual circuits for which it cannot guarantee the | |||
cannot guarantee the requested quality of service a-priori. Or | requested quality of service a priori. Alternatively, the network | |||
alternatively, the network pre-empts lower priority circuits to make | preempts lower-priority circuits to make room for a new circuit. | |||
room for the new one. | ||||
Quantum networks need a signaling function: once the path for a | Quantum networks need a signalling function: once the path for a QVC | |||
quantum virtual circuit has been computed, signaling is used to | has been computed, signalling is used to install the "forwarding | |||
install the "forwarding rules" into the data plane of each quantum | rules" into the data plane of each quantum router on the path. The | |||
router on the path. The signaling may be distributed, analogous to | signalling may be distributed, analogous to the Resource Reservation | |||
the resource reservation protocol (RSVP) in MPLS. Or the signaling | Protocol (RSVP) in MPLS. Or, the signalling may be centralised, | |||
may be centralized, similar to OpenFlow. | similar to OpenFlow. | |||
Quantum networks need an abstraction of the hardware for specifying | Quantum networks need an abstraction of the hardware for specifying | |||
the forwarding rules. This allows us to de-couple the control plane | the forwarding rules. This allows us to decouple the control plane | |||
(routing and signaling) from the data plane (actual creation of Bell | (routing and signalling) from the data plane (actual creation of Bell | |||
pairs). The forwarding rules are specified using abstract building | pairs). The forwarding rules are specified using abstract building | |||
blocks such as "creating local Bell pairs", "swapping Bell pairs", | blocks such as "creating local Bell pairs", "swapping Bell pairs", or | |||
"distillation of Bell pairs". As an analogy, classical networks use | "distillation of Bell pairs". As an analogy, classical networks use | |||
abstractions that are based on match conditions (e.g. looking up | abstractions that are based on match conditions (e.g., looking up | |||
header fields in tables) and actions (e.g. modifying fields or | header fields in tables) and actions (e.g., modifying fields or | |||
forwarding a packet to a specific interface). The data-plane | forwarding a packet to a specific interface). The data plane | |||
abstractions in quantum networks will be very different from those in | abstractions in quantum networks will be very different from those in | |||
classical networks due to the fundamental differences in technology | classical networks due to the fundamental differences in technology | |||
and the stateful nature of quantum networks. In fact, choosing the | and the stateful nature of quantum networks. In fact, choosing the | |||
right abstractions will be one of the biggest challenges when | right abstractions will be one of the biggest challenges when | |||
designing interoperable quantum network protocols. | designing interoperable quantum network protocols. | |||
In quantum networks, control plane traffic (routing and signaling | In quantum networks, control plane traffic (routing and signalling | |||
messages) is exchanged over a classical channel, whereas data plane | messages) is exchanged over a classical channel, whereas data plane | |||
traffic (the actual Bell pair qubits) is exchanged over a separate | traffic (the actual Bell pair qubits) is exchanged over a separate | |||
quantum channel. This is in contrast to most classical networks, | quantum channel. This is in contrast to most classical networks, | |||
where control plane traffic and data plane traffic share the same | where control plane traffic and data plane traffic share the same | |||
channel and where a single packet contains both user fields and | channel and where a single packet contains both user fields and | |||
header fields. There is, however, a classical analogy to the way | header fields. There is, however, a classical analogy to the way | |||
quantum networks work. Generalized MPLS (GMPLS) networks use | quantum networks work: generalised MPLS (GMPLS) networks use separate | |||
separate channels for control plane traffic and data plane traffic. | channels for control plane traffic and data plane traffic. | |||
Furthermore, GMPLS networks support data planes where there is no | Furthermore, GMPLS networks support data planes where there is no | |||
such thing as data plane headers (e.g. DWDM or TDM networks). | such thing as data plane headers (e.g., Dense Wavelength Division | |||
Multiplexing (DWDM) or Time-Division Multiplexing (TDM) networks). | ||||
8. Security Considerations | 8. Security Considerations | |||
Security is listed as an explicit goal for the architecture and this | Security is listed as an explicit goal for the architecture; this | |||
issue is addressed in the section on goals. However, as this is an | issue is addressed in Section 6.1. However, as this is an | |||
informational draft it does not propose any concrete mechanisms to | Informational document, it does not propose any concrete mechanisms | |||
achieve these goals. | to achieve these goals. | |||
9. IANA Considerations | 9. IANA Considerations | |||
This draft includes no request to IANA. | This document has no IANA actions. | |||
10. Acknowledgements | ||||
The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel | ||||
Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang, | ||||
Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG | ||||
community as a whole for their very useful reviews and comments to | ||||
the document. | ||||
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Acknowledgements | ||||
The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel | ||||
Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang, | ||||
Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG | ||||
community as a whole for their very useful reviews and comments on | ||||
this document. | ||||
WK and SW acknowledge funding received from the EU Flagship on | ||||
Quantum Technologies, Quantum Internet Alliance (No. 820445). | ||||
rdv acknowledges support by the Air Force Office of Scientific | ||||
Research under award number FA2386-19-1-4038. | ||||
Authors' Addresses | Authors' Addresses | |||
Wojciech Kozlowski | Wojciech Kozlowski | |||
QuTech | QuTech | |||
Building 22 | Building 22 | |||
Lorentzweg 1 | Lorentzweg 1 | |||
2628 CJ Delft | 2628 CJ Delft | |||
Netherlands | Netherlands | |||
Email: w.kozlowski@tudelft.nl | Email: w.kozlowski@tudelft.nl | |||
Stephanie Wehner | Stephanie Wehner | |||
QuTech | QuTech | |||
Building 22 | Building 22 | |||
Lorentzweg 1 | Lorentzweg 1 | |||
2628 CJ Delft | 2628 CJ Delft | |||
Netherlands | Netherlands | |||
Email: s.d.c.wehner@tudelft.nl | Email: s.d.c.wehner@tudelft.nl | |||
Rodney Van Meter | Rodney Van Meter | |||
Keio University | Keio University | |||
5322 Endo, Kanagawa | 5322 Endo, Fujisawa, Kanagawa | |||
252-0882 | 252-0882 | |||
Japan | Japan | |||
Email: rdv@sfc.wide.ad.jp | Email: rdv@sfc.wide.ad.jp | |||
Bruno Rijsman | Bruno Rijsman | |||
Individual | Individual | |||
Email: brunorijsman@gmail.com | Email: brunorijsman@gmail.com | |||
Angela Sara Cacciapuoti | Angela Sara Cacciapuoti | |||
University of Naples Federico II | University of Naples Federico II | |||
skipping to change at page 46, line 4 ¶ | skipping to change at line 2156 ¶ | |||
Italy | Italy | |||
Email: angelasara.cacciapuoti@unina.it | Email: angelasara.cacciapuoti@unina.it | |||
Marcello Caleffi | Marcello Caleffi | |||
University of Naples Federico II | University of Naples Federico II | |||
Department of Electrical Engineering and Information Technologies | Department of Electrical Engineering and Information Technologies | |||
Claudio 21 | Claudio 21 | |||
80125 Naples | 80125 Naples | |||
Italy | Italy | |||
Email: marcello.caleffi@unina.it | Email: marcello.caleffi@unina.it | |||
Shota Nagayama | Shota Nagayama | |||
Mercari, Inc. | Mercari, Inc. | |||
Roppongi Hills Mori Tower 18F | Roppongi Hills Mori Tower 18F | |||
6-10-1 Roppongi, Minato-ku, | 6-10-1 Roppongi, Minato-ku, Tokyo | |||
106-6118 | 106-6118 | |||
Japan | Japan | |||
Email: shota.nagayama@mercari.com | Email: shota.nagayama@mercari.com | |||
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