<?xml version="1.0"encoding="US-ASCII"?> <!-- This template is for creating an Internet Draft using xml2rfc, which is available here: http://xml.resource.org. -->encoding="UTF-8"?> <!DOCTYPE rfcSYSTEM "rfc2629.dtd"[<!-- One method to get references from the online citation libraries. There has to be one entity for each item to be referenced. 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(Here they are set differently than their defaults in xml2rfc v1.32) --> <?rfc strict="yes" ?> <!-- give errors regarding ID-nits and DTD validation --> <!-- control the table of contents (ToC) --> <?rfc toc="yes"?> <!-- generate a ToC --> <?rfc tocdepth="3"?> <!-- the number of levels of subsections in ToC. default: 3 --> <!-- control references --> <?rfc symrefs="yes"?> <!-- use symbolic references tags, i.e, [RFC2119] instead of [1] --> <?rfc sortrefs="yes" ?> <!-- sort the reference entries alphabetically --> <!-- control vertical white space (using these PIs as follows is recommended by the RFC Editor) --> <?rfc compact="yes" ?> <!-- do not start each main section on a new page --> <?rfc subcompact="no" ?> <!-- keep one blank line between list items --> <!-- end of list of popular I-D processing instructions --><rfc xmlns:xi="http://www.w3.org/2001/XInclude" submissionType="IRTF" category="info" consensus="true" docName="draft-irtf-qirg-principles-11"ipr="trust200902"> <!-- category values: std, bcp, info, exp, and historic ipr values: trust200902, noModificationTrust200902, noDerivativesTrust200902, or pre5378Trust200902 you can add the attributes updates="NNNN" and obsoletes="NNNN" they will automatically be output with "(if approved)" -->number="9340" ipr="trust200902" obsoletes="" updates="" xml:lang="en" tocInclude="true" tocDepth="3" symRefs="true" sortRefs="true" version="3"> <!--***** FRONT MATTER *****xml2rfc v2v3 conversion 3.15.0 --> <front><!-- The abbreviated title is used in the page header - it is only necessary if the full title is longer than 39 characters --><title abbrev="Principles for a Quantum Internet">Architectural Principles for a Quantum Internet</title><!-- add 'role="editor"' below for the editors if appropriate --> <!-- Another author who claims to be an editor --><seriesInfo name="RFC" value="9340"/> <author fullname="Wojciech Kozlowski" initials="W" surname="Kozlowski"> <organization>QuTech</organization> <address> <postal><street>Building 22</street><extaddr>Building 22</extaddr> <street>Lorentzweg 1</street><!-- Reorder these if your country does things differently --><code>2628 CJ</code> <city>Delft</city><region></region><country>Netherlands</country> </postal> <email>w.kozlowski@tudelft.nl</email><!-- uri and facsimile elements may also be added --></address> </author> <author fullname="Stephanie Wehner" initials="S" surname="Wehner"> <organization>QuTech</organization> <address> <postal><street>Building 22</street><extaddr>Building 22</extaddr> <street>Lorentzweg 1</street><!-- Reorder these if your country does things differently --><code>2628 CJ</code> <city>Delft</city><region></region><country>Netherlands</country> </postal> <email>s.d.c.wehner@tudelft.nl</email><!-- uri and facsimile elements may also be added --></address> </author> <author fullname="Rodney Van Meter" initials="R" surname="Van Meter"> <organization>Keio University</organization> <address> <postal> <street>5322Endo</street> <!-- Reorder these if your country does things differently --> <city>Fujisawa</city>Endo, Fujisawa</street> <region>Kanagawa</region> <code>252-0882</code> <country>Japan</country> </postal> <email>rdv@sfc.wide.ad.jp</email><!-- uri and facsimile elements may also be added --></address> </author> <author fullname="Bruno Rijsman" initials="B" surname="Rijsman"> <organization>Individual</organization> <address> <email>brunorijsman@gmail.com</email> </address> </author> <author fullname="Angela Sara Cacciapuoti" initials="A" surname="S. Cacciapuoti"> <organization>University of Naples Federico II</organization> <address> <postal><street>Department<extaddr>Department of Electrical Engineering and InformationTechnologies</street>Technologies</extaddr> <street>Claudio 21</street><!-- Reorder these if your country does things differently --><code>80125</code> <city>Naples</city> <country>Italy</country> </postal> <email>angelasara.cacciapuoti@unina.it</email><!-- uri and facsimile elements may also be added --></address> </author> <author fullname="Marcello Caleffi" initials="M" surname="Caleffi"> <organization>University of Naples Federico II</organization> <address> <postal><street>Department<extaddr>Department of Electrical Engineering and InformationTechnologies</street>Technologies</extaddr> <street>Claudio 21</street><!-- Reorder these if your country does things differently --><code>80125</code> <city>Naples</city> <country>Italy</country> </postal> <email>marcello.caleffi@unina.it</email><!-- uri and facsimile elements may also be added --></address> </author> <author fullname="Shota Nagayama" initials="S" surname="Nagayama"> <organization>Mercari, Inc.</organization> <address> <postal><street>Roppongi<extaddr>Roppongi Hills Mori Tower18F</street>18F</extaddr> <street>6-10-1 Roppongi, Minato-ku</street><!-- Reorder these if your country does things differently --><code>106-6118</code><city>Tokyo</city><region>Tokyo</region> <country>Japan</country> </postal> <email>shota.nagayama@mercari.com</email><!-- uri and facsimile elements may also be added --></address> </author> <dateyear="2022"year="2023" month="February" /><!-- If the month and year are both specified and are the current ones, xml2rfc will fill in the current day for you. If only the current year is specified, xml2rfc will fill in the current day and month for you. If the year is not the current one, it is necessary to specify at least a month (xml2rfc assumes day="1" if not specified for the purpose of calculating the expiry date). With drafts it is normally sufficient to specify just the year. --> <!-- Meta-data Declarations --> <area>General</area><workgroup>QuantumInternet Research Group</workgroup> <!-- WG name at the upperleft corner of the doc, IETF is fine for individual submissions. If this element is not present, the default is "Network Working Group", which is used by the RFC Editor as a nod to the history of the IETF. -->Internet</workgroup> <keyword>Quantum Internet</keyword> <keyword>Architecture</keyword> <keyword>Repeater</keyword> <keyword>Bell Pair</keyword> <keyword>EPR Pair</keyword><!-- Keywords will be incorporated into HTML output files in a meta tag but they have no effect on text or nroff output. If you submit your draft to the RFC Editor, the keywords will be used for the search engine. --><abstract> <t>The vision of a quantum internet is to enhance existing Internet technology by enabling quantum communication between any two points on Earth. To achieve this goal, a quantum network stack should be built from the ground up to account for the fundamentally new properties of quantum entanglement. The first quantum entanglement networks have beenrealised <xref target="Pompili21.1" />,realised, but there is no practical proposal for how to organise, utilise, and manage such networks. In thisdraft,document, we attempt to lay down the framework and introduce some basic architectural principles for a quantum internet. This is intended for general guidance and generalinterest, butinterest. It is also intended to provide a foundation for discussion between physicists and network specialists. This document is a product of the Quantum Internet Research Group (QIRG).</t> </abstract> </front> <middle> <sectiontitle="Introduction">numbered="true" toc="default"> <name>Introduction</name> <t>Quantum networks are distributed systems of quantum devices that utilise fundamental quantum mechanical phenomena such as superposition, entanglement, and quantum measurement to achieve capabilities beyond what is possible with non-quantum (classical) networks <xref target="Kimble08"/>.format="default"/>. Depending on the stage of a quantum network <xref target="Wehner18"/>format="default"/>, such devices may range from simple photonic devices 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 quantum network is not meant to replace classicalnetworks,networks but rather to form an overall hybrid classical-quantum network supporting new capabilitieswhichthat are otherwise impossible to realise <xref target="VanMeterBook"/>.format="default"/>. For example, the most well-known application of quantum communication,quantum key distribution (QKD),Quantum Key Distribution (QKD) <xref target="QKD" format="default"/>, can create and 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 thus can be mathematically proven to be unbreakable) rather than the intractability of certain mathematical problems <xref target="Bennett14"/>format="default"/> <xref target="Ekert91"/>.format="default"/>. Small networks capable of QKD have even already been deployed at short (roughly100km)100-kilometre) distances <xref target="Elliott03"/>format="default"/> <xref target="Peev09"/>format="default"/> <xref target="Aguado19"/>format="default"/> <xref target="Joshi20"/>.</t>format="default"/>.</t> <t>The quantum networking paradigm also offers promise for a range of new applications beyond quantum cryptography, such as distributed quantum computation <xref target="Cirac99"/>format="default"/> <xref target="Crepeau02"/>,format="default"/>; secure quantum computing in the cloud <xref target="Fitzsimons17"/>,format="default"/>; quantum-enhanced measurement networks <xreftarget="Giovanetti04" />,target="Giovannetti04" format="default"/>; or higher-precision, long-baseline telescopes <xref target="Gottesman12"/>.format="default"/>. These applications are much more demanding thanQKDQKD, and networks capable of executing them are in their infancy. The first fully quantum, multinode network capable of sending, receiving, and manipulating distributed quantum information has only recently beenrealizedrealised <xref target="Pompili21.1"/></t>format="default"/>.</t> <t>Whilst a lot of effort has gone into physically realising and connecting such devices, and making improvements to their speed and error tolerance,there arenoworked outproposals for how to run thesenetworks.networks have been worked out at the time of this writing. To draw an analogy with a classical network, we are at a stage where we can start to physically connect our devices and send data, but all sending, receiving, buffer management, connection synchronisation, and soon,on must be managed by the application directly by using low-level, custom-built, and hardware-specific interfaces, rather than being managed by a network stack that exposes a convenient high-level interface, such as sockets. Onlyrecently,recently was thefirst everfirst-ever attempt at such a network stack experimentally demonstrated in a laboratory setting <xref target="Pompili21.2"/>.format="default"/>. Furthermore, whilst physical mechanisms for transmitting quantum information exist, there are no robust protocols for managing such transmissions.</t> <t>This document, produced by the Quantum Internet Research Group (QIRG), introduces quantum networks and presents general guidelines for the design and construction of such networks. Overall, it is intended as an introduction to the subject for network engineers and researchers. It should not be considered as a conclusive statement on how quantumnetworknetworks should or will be implemented. This document was discussed on the QIRG mailing list and several IETFmeetings andmeetings. It represents the consensus of the QIRG members,bothof both experts in the subject matter (from the quantumas welland networkingdomain) as well asdomains) and newcomers who are the target audience.</t> </section> <sectiontitle="Quantum information">numbered="true" toc="default"> <name>Quantum Information</name> <t>In order to understand the framework for quantum networking, a basic understanding of quantum information theory is necessary. The following sections aim to introduce the minimum amount of knowledge necessary to understand the principles of operation of a quantum network. This exposition was written with a classical networking audience in mind. It is assumed that the reader has never before been exposed to any quantum physics. We refer the reader to <xref target="SutorBook"/>format="default"/> and <xreftarget="NielsenChuang"/>target="NielsenChuang" format="default"/> for an in-depth introduction to quantum information systems.</t> <sectiontitle="Quantum state">numbered="true" toc="default"> <name>Quantum State</name> <t>A quantum mechanical system is described by its quantum state. A quantum state is an abstract object that provides a complete description of the system at that particular moment. When combined 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 at all times. For the purposes of computing and networking, the classical equivalent of a quantum state would be a string or stream of logical bit values. These bits provide a complete description of what values we can read out from that string at that particularmomentmoment, 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.</t> <t>Just like a single classical bit, a quantum mechanical system can be simple and consist of a single particle,e.g.e.g., an atom or a photon of light. In this case, the quantum state provides the complete description of that one particle. Similarly, just like a string of bits consists of multiple bits, a single quantum state can be used to also describe an ensemble of many particles. However, because quantum states are governed by the laws of quantummechanicsmechanics, their behaviour is significantly different to that of a string of bits. In thissectionsection, we will summarise the key concepts to understand thesedifferences and the wedifferences. We will then explain their consequences for networking in the rest ofthe draft.</t>this document.</t> </section> <sectiontitle="Qubit">numbered="true" toc="default"> <name>Qubit</name> <t>The differences between quantum computation and classical computation begin at thebit-level.bit level. A classical computer operates on the binary alphabet { 0, 1 }.A A quantum bit, called a qubit, exists over the same binary space, but unlike the classical bit, its state can exist in a superposition of the two possibilities:</t><t>|qubit><t>|qubit⟩ = a|0>|0⟩ + b|1>,</t>|1⟩,</t> <t>where|X>|X⟩ is Dirac's ket notation for a quantum state (the value that a qubitholds), hereholds) -- here, the binary 0 and1,1 -- and the coefficients a and b are complex numbers called probability amplitudes. Physically, such a state can be realised using a variety of different technologies such as electron spin, photon polarisation, atomic energy levels, and so on.</t> <t>Upon measurement, the qubit loses its superposition and irreversibly collapses into one of the two basis states, either|0>|0⟩ or|1>.|1⟩. Which of the two states it ends up in may not bedeterministic,deterministic but can be determined from the readout of the measurement. The measurement result is a classical bit, 0 or 1, corresponding to|0>|0⟩ and|1>|1⟩, respectively. The probability of measuring the state in the|0>|0⟩ state is|a|^2 and similarly|a|<sup>2</sup>; similarly, the probability of measuring the state in the|1>|1⟩ state is|b|^2,|&wj;b&wj;|&wj;<sup>2</sup>, where|a|^2|a|<sup>2</sup> +|b|^2|b|<sup>2</sup> = 1. This randomness is not due to our ignorance of the underlyingmechanisms,mechanisms but rather is a fundamental feature of a quantum mechanical system <xref target="Aspect81"/>.</t>format="default"/>.</t> <t>The superposition property plays an important role in fundamental gate operations on qubits. Since a qubit can exist in a superposition of its basis states, the elementary quantum gates are able to act on all states of the superposition at the same time. For example, consider the NOT gate:</t> <t>NOT (a|0>|0⟩ + b|1>) ->|1⟩) ➔ a|1>|1⟩ + b|0>.</t>|0⟩.</t> <t>It is important to note that "qubit" can have two meanings. In the first meaning, "qubit" refers to a physical quantum*system*<strong>system</strong> whose quantum state can be expressed as a superposition of two basis states, which we often label|0>|0⟩ and|1>.|1⟩. Here, "qubit" refers to a physical implementation akin to what a flip-flop, switch, voltage, or current would be for a classical bit. In the second meaning, "qubit" refers to the abstract quantum*state*<strong>state</strong> of a quantum system with such two basis states. In this case, the meaning of "qubit" is akin to the logical value of a bit, from classical computing,i.e.i.e., "logical 0" or "logical 1". The two concepts are related, because a physical "qubit" (first meaning) can be used to store the abstract "qubit" (second meaning). Both meanings are used interchangeably inliteratureliterature, and the meaning is generally clear from the context.</t> </section> <sectiontitle="Multiple qubits">numbered="true" toc="default"> <name>Multiple Qubits</name> <t>When multiple qubits are combined in a single quantumstatestate, the space of possible states grows exponentially and all these states can coexist in a superposition. For example, the general form of a two-qubit register is</t> <t>a|00>|00⟩ + b|01>|01⟩ + c|10>|10⟩ + d|11></t>|11⟩,</t> <t>where the coefficients have the same probability amplitude interpretation as for thesingle qubitsingle-qubit state. Each state represents a possible outcome of a measurement of the two-qubit register. For example,|01>|01⟩ denotes a state in which the first qubit is in the state|0>|0⟩ and the second is in the state|1>.</t>|1⟩.</t> <t>Performingsingle qubitsingle-qubit gates affects the relevant qubit in each of the superposition states. Similarly, two-qubit gates also act on all the relevant superposition states, but their outcome is far more interesting.</t> <t>Consider a two-qubit register where the first qubit is in the superposed state(|0>(|0⟩ +|1>)/sqrt(2)|1⟩)/sqrt(2) and the other is in the state|0>.|0⟩. This combined state can be writtenas:</t> <t>(|0>as</t> <t>(|0⟩ +|1>)/sqrt(2)|1⟩)/sqrt(2) x|0>|0⟩ =(|00>(|00⟩ +|10>)/sqrt(2),</t>|10⟩)/sqrt(2),</t> <t>where x denotes a tensor product (the mathematical mechanism for combining quantum states together).</t> <t>The constant 1/sqrt(2) is called the normalisation factor and reflects the fact that the probabilities of measuring either a|0>|0⟩ or a|1>|1⟩ for the first qubit add up to one.</t> <t>Let us now consider the two-qubitcontrolled-NOT,Controlled NOT, or CNOT, gate. The CNOT gate takes as input twoqubits,qubits -- a control andtarget,a target -- and applies the NOT gate to the target if the control qubit is set. The truth table looks like</t><texttable> <ttcol align="center">IN</ttcol> <ttcol align="center">OUT</ttcol> <c>00</c><c>00</c> <c>01</c><c>01</c> <c>10</c><c>11</c> <c>11</c><c>10</c> </texttable><table align="center"> <name>CNOT Truth Table</name> <thead> <tr> <th align="center">IN</th> <th align="center">OUT</th> </tr> </thead> <tbody> <tr> <td align="center">00</td> <td align="center">00</td> </tr> <tr> <td align="center">01</td> <td align="center">01</td> </tr> <tr> <td align="center">10</td> <td align="center">11</td> </tr> <tr> <td align="center">11</td> <td align="center">10</td> </tr> </tbody> </table> <t>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 superposition states:</t> <t>CNOT(|00>(|00⟩ +|10>)/sqrt(2) -> (|00>|10⟩)/sqrt(2) ➔ (|00⟩ +|11>)/sqrt(2).</t>|11⟩)/sqrt(2).</t> <t>What is so interesting about this two-qubit gate operation? The final state is*entangled*. There<strong>entangled</strong>. There is no possible way of representing that quantum state as a product of two individual qubits; they are no longer independent. That is, it is not possible to describe the 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 that consists of both qubits provides a physically complete description of the two-qubit system. The states of the two individual qubits are now correlated beyond what is possible to achieve classically. Neither qubit is in a definite|0>|0⟩ or|1>|1⟩ state, but if we perform a measurement on either one, the outcome of the partner qubit will*always*<strong>always</strong> yield the exact same outcome. The final state, whether it's|00>|00⟩ or|11>,|11⟩, is fundamentally random as before, but the states of the two qubits following a measurement will always be identical. One can think of this as flipping two coins, buttheboth coins alwaysbothland on "heads" or both land on "tails"together. Somethingtogether -- something that we know is impossible classically.</t> <t>Once a measurement is performed, the two qubits are once again independent. The final state is either|00>|00⟩ or|11>|11⟩, and both of these states can be trivially decomposed into a product of two individual qubits. The entanglement has beenconsumedconsumed, and the entangled state must be prepared again.</t> </section> </section> <section anchor="entanglement"title="Entanglementnumbered="true" toc="default"> <name>Entanglement as thefundamental resource">Fundamental Resource</name> <t>Entanglement is the fundamental building block of quantum networks. Consider the state from the previous section:</t><t>(|00><t>(|00⟩ +|11>)/sqrt(2).</t>|11⟩)/sqrt(2).</t> <t>Neither of the two qubits is in a definite|0>|0⟩ or|1> state|1⟩ state, and we need to know the state of the entire register to be able to fully describe the behaviour of the two qubits.</t> <t>Entangled qubits have interesting non-local properties. Consider 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 country, or even on a different planet. Provided negligible noise has been introduced, the two qubits will forever remain in the entangled state until a measurement is performed. The physical distance does not matter at all for entanglement.</t> <t>This lies at the heart of quantum networking, because it is possible to leverage the non-classical correlations provided by entanglement in order to design completely new types of application protocols that are not possible to achieve with just classical communication. Examples of such applications are quantum cryptography <xref target="Bennett14"/>format="default"/> <xref target="Ekert91"/>,format="default"/>, blind quantum computation <xref target="Fitzsimons17"/>,format="default"/>, or distributed quantum computation <xref target="Crepeau02"/>.</t>format="default"/>.</t> <t>Entanglement has two very special features from which one can derive some intuition about the types of applications enabled by a quantum network.</t> <t>The first stems from the fact that entanglement enablesstronger than classicalstronger-than-classical correlations, leading to opportunities for tasks that require coordination. As a trivial example, consider the problem of 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(|00>(|00⟩ +|11>)/sqrt(2)|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 two qubits collapses to either|00>|00⟩ or|11>,|11⟩, so whilst the outcome is random and does not exist before measurement, the two nodes will always measure the same value. We can also build the more general multi-qubit state(|00...>(|00...⟩ +|11...>)/sqrt(2)|11...⟩)/sqrt(2) and perform the same algorithm between an arbitrary number of nodes. Thesestronger than classicalstronger-than-classical correlations generalise tomore complicatedmeasurement schemes that are more complicated as well.</t> <t>The second feature of entanglement is that it cannot be shared, in the sense that if two qubits are maximally entangled with each other, then it is physically impossible for these two qubits to also be entangled with a third qubit <xref target="Terhal04"/>.format="default"/>. Hence, entanglement forms a sort of private and inherently untappable connection between two nodes once established.</t> <t>Entanglement is created through local interactions between two qubits or as a product of the way the qubits were created(e.g.(e.g., entangled photon pairs). To create a distributed entangled state, one can then physically send one of the qubits to a remote node. It is also possible to directly entangle qubits that are physically separated, but this still requires local interactions between some other qubits that the separated qubits are initially entangled with. Therefore, it is the transmission of qubits that draws the line between a genuine quantum network and a collection of quantum computers connected over a classical network.</t> <t>A quantum network is defined as a collection of nodes that is able to exchange qubits and distribute entangled states amongst themselves. A quantum node that is able only to communicate classically with another quantum node is not a member of a quantum network.</t><t>More complex services<t>Services and applications that are more complex can be built on top of entangled states distributed by thenetwork,network; for example, seee.g.<xref target="ZOO"/></t>format="default"/>.</t> </section> <sectiontitle="Achieving quantum connectivity">numbered="true" toc="default"> <name>Achieving Quantum Connectivity</name> <t>This section explains the meaning of quantum connectivity and the necessary physical processes at an abstract level.</t> <sectiontitle="Challenges">numbered="true" toc="default"> <name>Challenges</name> <t>A quantum network cannot be built by simply extrapolating all the classical models to their quantum analogues. Sending qubits over a wire like we send classical bits is simply not as easy to do. There are several technological as well as fundamental challenges that make classical approaches unsuitable in a quantum context.</t> <sectiontitle="The measurement problem">numbered="true" toc="default"> <name>The Measurement Problem</name> <t>In classical computers andnetworksnetworks, we can read out the bits stored 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 not possible with qubits.</t> <t>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 being processed, it cannot be read out until a suitable point in the computation, determined by the protocol handling the qubit, has been reached. Therefore, we cannot use the same methods known from classical computing for the purposes of error detection and correction. Nevertheless, quantum error detection and correction schemes exist that take this problem intoaccountaccount, and how a network chooses to manage errors will have an impact on its architecture.</t> </section> <sectiontitle="No-cloning theorem">numbered="true" toc="default"> <name>No-Cloning Theorem</name> <t>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. Unfortunately, this is fundamentally not possible in quantum mechanics <xref target="Park70"/>format="default"/> <xref target="Wootters82"/>.</t>format="default"/>.</t> <t>The no-cloning theorem states that it is impossible to create an identical copy of an arbitrary, unknown quantum state. Therefore, it is also impossible to use the same mechanisms that worked for classical networks for signal amplification, retransmission, and soonon, as they all rely on the ability to copy the underlying data. Since any physical channel will always be lossy, connecting nodes within a quantum network is a challengingendeavourendeavour, and its architecture must at its core address this very issue.</t> </section> <section anchor="fidelity"title="Fidelity">numbered="true" toc="default"> <name>Fidelity</name> <t>In general, it is expected that a classical packet arrives at its destination without any errors introduced by hardware noise along the way. This is verified at various levels through a variety of error detection and correction mechanisms. Since we cannot read or copy a quantum state, error detection and correctionisare more involved.</t> <t>To describe the quality of a quantum state, a physical quantity called fidelity is used <xref target="NielsenChuang"/>.format="default"/>. Fidelity takes a value 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 we have tried to create. It expresses the probability that the state will behave exactly the same as our desired state. Fidelity is an important property of a quantum system that allows us to quantify how much a particular state has been affected by noise from various sources (gate errors, channel losses, environment noise).</t> <t>Interestingly, quantum applications do not need perfect fidelity to be able to execute -- as long as the fidelity is above some application-specific threshold, they will simply operate at lower rates. Therefore, rather than trying to ensure that we always deliver perfect states (a technologically challengingtask)task), applications will specify a minimum threshold for thefidelityfidelity, and the network will try its best to deliver it. A higher fidelity can be achieved by either having hardware produce states of better fidelity (sometimes one can sacrifice rate for higher fidelity) orbyemploying quantum error detection and correction mechanisms (see <xref target="Mural16"/>format="default"/> and Chapter 11 of <xref target="VanMeterBook"/> chapter 11).</t>format="default"/>).</t> </section> <section anchor="dt"title="Inadequacynumbered="true" toc="default"> <name>Inadequacy ofdirect transmission">Direct Transmission</name> <t>Conceptually, the most straightforward way to distribute an entangled state is to simply transmit one of the qubits directly to the other end across a series of nodes while performing sufficient forwardquantum error correctionQuantum Error Correction (QEC) (<xref target="qec"/>)format="default"/>) to bring losses down to an acceptable level. Despite the no-cloning theorem and the inability to directly measure a quantum state, error-correcting mechanisms for quantum communication exist <xref target="Jiang09"/>format="default"/> <xref target="Fowler10"/>format="default"/> <xref target="Devitt13"/>format="default"/> <xref target="Mural16"/>.format="default"/>. However,quantum error correctionQEC makes very high demands on both resources (physical qubits needed) and their initial fidelity. Implementation is verychallengingchallenging, andquantum error correctionQEC is not expected to be used until later generations of quantum networks are possible (see Figure 2 of <xref target="Mural16"/> figure 2format="default"/> and <xref target="generations"/>).format="default"/> of this document). Until then, quantum networks rely on entanglement swapping (<xref target="es"/>)format="default"/>) and teleportation (<xref target="teleportation"/>).format="default"/>). This alternative relies on the observation that we do not need to be able to distribute any arbitrary entangled quantum state. We only need to be able to distribute any one of what are known as the Bell pair states <xref target="Briegel98"/>.</t>format="default"/>.</t> </section> </section> <sectiontitle="Bell pairs">numbered="true" toc="default"> <name>Bell Pairs</name> <t>Bell pair states are the entangled two-qubit states:</t><t> |00><artwork align="left" name="" type="" alt=""><![CDATA[ |00⟩ +|11>, |00>|11⟩, |00⟩ -|11>, |01>|11⟩, |01⟩ +|10>, |01>|10⟩, |01⟩ -|10>, </t>|10⟩, ]]></artwork> <t>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 is possible to transform any Bell pair into another Bell pair with 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 apply a series ofsingle qubitsingle-qubit gates to their qubit alone in order to transform the state between the different variants.</t> <t>Distributing a Bell pair between two nodes is much easier than transmitting an arbitrary quantum state over a network. Since the state is known, handling errors becomeseasiereasier, and small-scaleerror-correctionerror correction (such as entanglementdistillationdistillation, as discussed ina later section)<xref target="ent-dis"/>), combined withreattemptsreattempts, becomes a valid strategy.</t> <t>The reason for using Bell pairs specifically as opposed to any other two-qubit state is that they are the maximally entangled two-qubit set of basis states. Maximal entanglement means that these states have the strongest non-classical correlations of all possible two-qubit states. Furthermore, since single-qubit local operations can never increase entanglement, states that are less entangledstateswould impose some constraints on distributed quantum algorithms. This makes Bell pairs particularly useful as a generic building block for distributed quantum applications.</t> </section> <section anchor="teleportation"title="Teleportation">numbered="true" toc="default"> <name>Teleportation</name> <t>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 arbitrary entangled state. This can be achieved via quantum state teleportation <xref target="Bennett93"/>.format="default"/>. Quantum state teleportation consumes an unknown qubit state that we want to transmit and recreates it at the desired destination. This does not violate the no-cloningtheoremtheorem, as the original state is destroyed in the process.</t> <t>To achieve this, an entangled pair needs to be distributed between the source and destination before teleportation commences. The source then entangles the transmission qubit with its end of the pair and performs aread outreadout of the two qubits (the sum of these operations is called a Bell state measurement). This consumes the Bell pair's entanglement, turning the source and destination qubits into independent states. Themeasurementsmeasurement yields two classicalbitsbits, which the source sends to the destination over a classical channel. Based on the value of the received two classical bits, the destination performs one of four possible corrections (called the Pauli corrections) on its end of the pair, which turns it into the unknown qubit state that we wanted to transmit. This requirement to communicate the measurementread outreadout over a classical channel unfortunately means that entanglement cannot be used to transmit information faster than the speed of light.</t> <t>The unknown quantum state that was transmitted was never fed into the network itself. Therefore, the network needs to only be able to reliably produce Bell pairs between any two nodes in the network. Thus, a key difference between a classical data plane and a quantum dataplanesplane is that a classicalonedata plane carries userdata,data but a quantum data plane provides the resources for the user to transmit user data themselves without further involvement of the network.</t> </section> <sectiontitle="The life cyclenumbered="true" toc="default"> <name>The Life Cycle ofentanglement">Entanglement</name> <t>Reducing the problem of quantum connectivity to one of generating a Bell pair hasfacilitatedreduced theproblem,problem to a simpler, more fundamental case, but it has not solved it. In this section, we discuss how these entangled pairs are generated in the firstplace,place and how their two qubits are delivered to the end-points.</t> <section anchor="elg"title="Elementary link generation">numbered="true" toc="default"> <name>Elementary Link Generation</name> <t>In a quantum network, entanglement is always first generated locally (at a node or an auxiliaryelement)element), followed by a movement of one or both of the entangled qubits across the link through quantum channels. In this context, photons (particles of light) are the natural candidate for entanglementcarriers, calledcarriers. Because these photons carry quantum states from place to place at high speed, we call them flying qubits. The rationale for this choice is related to the advantages provided byphotonsphotons, such as moderate interaction with the environment leading to moderatedecoherence,decoherence; convenient control with standard opticalcomponents,components; and high-speed, low-loss transmissions. However, since photons are hard to store, a transducer must transfer the flying qubit's state to a qubit suitable for information processing and/or storage (often referred to as a matter qubit).</t> <t>Since this process may fail, in order to generate and store entanglement efficiently, we must be able to distinguish successful attempts from failures. Entanglement generation schemes that are able to announce successful generation are called heralded entanglement generation schemes.</t> <t>There exist three basic schemes for heralded entanglement generation on a link through coordinated action of the two nodes at the two ends of the link <xref target="Cacciapuoti19"/>:</t> <t> <list style="symbols"> <t>"At mid-point": informat="default"/>:</t> <dl spacing="normal"> <dt>"At mid-point":</dt><dd>In thisschemescheme, an entangled photon pair source sitting midway between the two nodes with matter qubits sends an entangled photon through a quantum channel to each of the nodes. There, transducers are invoked to transfer the entanglement from the flying qubits to the matter qubits. In this scheme, the transducers know if the transfers succeeded and are able to herald successful entanglement generation via a message exchange over the classicalchannel.</t> <t>"At source": inchannel.</dd> <dt>"At source":</dt><dd>In thisschemescheme, one of the two nodes sends a flying qubit that is entangled with one of its matter qubits. A transducer at the other end of the link will transfer the entanglement from the flying qubit to one of its matter qubits. Just like in the previous scheme, the transducer knows if its transfer succeeded and is able to herald successful entanglement generation with a classical message sent to the othernode.</t> <t>"Atnode.</dd> <dt>"At bothend-points": inend-points":</dt><dd>In thisschemescheme, both nodes send a flying qubit that is entangled with one of their matter qubits. A detector somewhere in between the nodes performs a joint measurement on thetwoflying qubits, which stochastically projects the remote matter qubits into an entangled quantum state. The detector knows if the entanglement succeeded and is able to herald successful entanglement generation by sending a message to each node over the classicalchannel.</t> </list> </t>channel.</dd> </dl> <t>The "mid-point source" scheme is more robust to photon loss, but in the otherschemesschemes, the nodes retain greater control over the entangled pair generation.</t> <t> Note that whilst photons travel in a particular direction through the quantum channel the resulting entangled pair of qubits does not have a direction associated with it. Physically, there is no upstream or downstream end of the pair.</t> </section> <section anchor="es"title="Entanglement swapping">numbered="true" toc="default"> <name>Entanglement Swapping</name> <t>The problem with generating entangled pairs directly across a link is that efficiency decreases with channel length. Beyond a few10stens of kilometres in optical fibre or 1000 kilometres in free space (viasatellite)satellite), the rate is effectivelyzerozero, and due to the no-cloning theorem we cannot simply amplify the signal. The solution is entanglement swapping <xref target="Briegel98"/>.</t>format="default"/>.</t> <t>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 between the two end-points. Each node along the path can consume the two pairs on the two linksthatto which it isconnected toconnected, in order to produce a new entangled pair between the two remote ends. This process is known as entanglement swapping.Pictorially itIt can be represented pictorially as follows:</t><figure align="center"><artworkalign="left"><![CDATA[align="left" name="" type="" alt=""><![CDATA[ +---------+ +---------+ +---------+ | A | | B | | C | | |------| |------| | | X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 | +---------+ +---------+ +---------+ ]]></artwork></figure><t>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 ~~.In 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.</t> <t>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 qubits X2 and Y1which resultthat results in the destruction of the entanglement between Y1 and Y2. However, X2 is recreated in Y2's place, carrying with it its entanglement with X1. Theend-resultend result is shown below:</t><figure align="center"><artworkalign="left"><![CDATA[align="left" name="" type="" alt=""><![CDATA[ +---------+ +---------+ +---------+ | A | | B | | C | | |------| |------| | | X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 | +---------+ +---------+ +---------+ ]]></artwork></figure><t>Depending on the needs of the network and/or application, a final Pauli correction at the recipient node may not benecessarynecessary, since the result of this operation is also a Bell pair. However, the two classical bits that form theread outreadout from the measurement at node B must still be communicated, because they carry information about which of the four Bell pairs was actually produced. If a correction is not performed, the recipient must be informed which Bell pair was received.</t> <t>This process of teleporting Bell pairs using other entangled pairs is called entanglement swapping. Quantum nodes that create long-distance entangled pairs via entanglement swapping are called quantum repeaters in academic literature <xref target="Briegel98"/> and weformat="default"/>. We will use the same terminology in thisdraft.</t>document.</t> </section> <sectiontitle="Error Management">numbered="true" toc="default"> <name>Error Management</name> <section anchor="ent-dis"title="Distillation">numbered="true" toc="default"> <name>Distillation</name> <t>Neither the generation of Bell pairs nor the swapping operations are noiseless operations. Therefore, with each link and eachswapswap, the fidelity of the state degrades. However, it is possible to createhigher fidelityhigher-fidelity Bell pair states from two or morelower fidelitylower-fidelity pairs through a process called distillation (sometimes also referred to as purification) <xref target="Dur07"/>.</t>format="default"/>.</t> <t>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, e.g., "the parity of the two qubits in the first state is even." When the test succeeds, confidence in the state is improved, and thus the fidelity is improved. The test tool states are destroyed in the process, so resource demands increase substantially when distillation is used. When the test fails, the tested state must also be discarded. Distillation makes low demands on fidelity and resources compared toquantum error correction,QEC, but distributed protocols incur round-trip delays due to classical communication <xref target="Bennett96"/>.</t>format="default"/>.</t> </section> <section anchor="qec"title="Quantumnumbered="true" toc="default"> <name>Quantum ErrorCorrection">Correction (QEC)</name> <t>Just like classical error correction,quantum error correction (QEC)QEC encodes logical qubits using several physical (raw) qubits to protect them from the errors described in <xref target="fidelity"/>format="default"/> <xref target="Jiang09"/>format="default"/> <xref target="Fowler10"/>format="default"/> <xref target="Devitt13"/>format="default"/> <xref target="Mural16"/>.format="default"/>. Furthermore, similarly to its classical counterpart, QEC can not only correct state errors but also account for lost qubits. Additionally, if all physical qubitswhichthat encode a logical qubit are located at the same node, the correction procedure can be executed locally, even if the logical qubit is entangled with remote qubits.</t> <t>Although QEC was originally a scheme proposed to protect a qubit from noise, QEC can also be applied to entanglement distillation. Such QEC-applied distillation iscost-effectivecost effective but requires a higher base fidelity.</t> </section> <section anchor="generations"title="Error management schemes">numbered="true" toc="default"> <name>Error Management Schemes</name> <t>Quantum networks have beencategorizedcategorised into three "generations" based on the error management scheme they employ <xref target="Mural16"/>.format="default"/>. Note that these "generations" are more like categories; they do not necessarily imply a time progression and do not obsolete each other, though the later generations do require technologies that are moreadvanced technologies.advanced. Which generation is used depends on the hardware platform and network design choices.</t> <t><xref target="gens"/>format="default"/> summarises the generations.</t><texttable<table anchor="gens"title="Classical signalingalign="center"> <name>Classical Signalling andgenerations"> <ttcol align="center"></ttcol> <ttcolGenerations</name> <thead> <tr> <th align="center"/> <th align="center">Firstgeneration</ttcol> <ttcolgeneration</th> <th align="center">Secondgeneration</ttcol> <ttcolgeneration</th> <th align="center">Thirdgeneration</ttcol> <c>Loss tolerance</c> <c>Heraldedgeneration</th> </tr> </thead> <tbody> <tr> <td align="center">Loss tolerance</td> <td align="center">Heralded entanglement generation(bi-directional(bidirectional classicalsignaling)</c> <c>Heraldedsignalling)</td> <td align="center">Heralded entanglement generation(bi-directional(bidirectional classicalsignaling)</c> <c>Quantum Error Correctionsignalling)</td> <td align="center">QEC (no classicalsignaling)</c> <c></c> <c></c> <c></c> <c></c> <c>Error tolerance</c> <c>Entanglementsignalling)</td> </tr> <tr> <td align="center"/> <td align="center"/> <td align="center"/> <td align="center"/> </tr> <tr> <td align="center">Error tolerance</td> <td align="center">Entanglement distillation(bi-directional(bidirectional classicalsignaling)</c> <c>Entanglementsignalling)</td> <td align="center">Entanglement distillation(uni-directional(unidirectional classicalsignaling)signalling) orQuantum Error CorrectionQEC (no classicalsignaling) </c> <c>Quantum Error Correctionsignalling) </td> <td align="center">QEC (no classicalsignaling)</c> </texttable>signalling)</td> </tr> </tbody> </table> <t>Generations are defined by the directions of classical signalling required in their distributed protocols for loss tolerance and error tolerance. Classical signalling carries the classicalbits and incursbits, incurring round-tripdelaysdelays. As described in <xref target="ent-dis"/>, hence theyformat="default"/>, these delays affect the performance of quantum networks, especially as the distance between the communicating nodes increases.</t> <t>Loss tolerance is about tolerating qubit transmission losses between nodes. Heralded entanglement generation, as described in <xref target="elg"/>,format="default"/>, confirms the receipt of an entangled qubit using a heralding signal. A pair of directly connected quantum nodes repeatedly attempt to generate an entangled pair until theaheralding signal is received. As described in <xref target="qec"/>,format="default"/>, QEC can be applied to complement lostqubitsqubits, eliminating the need forre-attempts.reattempts. Furthermore, since the correction procedure is composed of local operations, it does not require a heralding signal. However, it is possible only when the photon loss rate from transmission to measurement is less than 50%.</t> <t>Error tolerance is about tolerating quantum state errors. Entanglement distillation is the easiest mechanism to implement for improved errortolerance to implement,tolerance, but it incurs round-trip delays due to the requirement forbi-directionalbidirectional classical signalling. The alternative, QEC, is able to correct state errors locally so that it does not need any classical signalling between the quantum nodes. In between these two extremes, there is also QEC-applied distillation, which requiresuni-directionalunidirectional classical signalling.</t> <t>The three "generations" summarised:</t><t> <list style="numbers"> <t>First generation<ol spacing="normal" type="1"><li>First-generation quantum networks use heralding for loss tolerance and entanglement distillation for error tolerance. These networks can be implemented even with a limited set of available quantumgates.</t> <t>Second generationgates.</li> <li>Second-generation quantum networks improve upon the first generation with QEC codes for error tolerance (but not loss tolerance). At first, QEC will be applied to entanglement distillationonlyonly, which requiresuni-directionalunidirectional classical signalling. Later, QEC codes will be used to create logical Bell pairswhichthat no longer require any classical signalling for the purposes of error tolerance. Heralding is still used to compensate for transmissionlosses.</t> <t>Third generationlosses.</li> <li>Third-generation quantum networks directly transmitQEC encodedQEC-encoded qubits to adjacent nodes, as discussed in <xref target="dt"/>.format="default"/>. Elementary link Bell pairs can now be created without heralding or any other classical signalling. Furthermore, this also enables direct transmission architectures in which qubits are forwardedend-to-endend to end like classical packets rather than relying on Bell pairs and entanglementswapping.</t> </list> </t>swapping.</li> </ol> <t>Despite the fact that there are important distinctions in how errors will be managed in the differentgenerationsgenerations, it is unlikely that all quantum networks will consistently use the same method. This is due to different hardware requirements of the different generations and the practical reality of network upgrades. Therefore, it is unavoidable that eventually boundaries between different error management schemes start forming. This will affect the content and semantics of messages that must cross those boundaries --bothfor both connection setup and real-time operation <xref target="Nagayama16"/>.</t>format="default"/>.</t> </section> </section> <sectiontitle="Delivery">numbered="true" toc="default"> <name>Delivery</name> <t>Eventually, the Bell pairs must be delivered to an application (orhigher layerhigher-layer protocol) at the twoend-nodes.end nodes. A detailed list of such requirements is beyond the scope of thisdraft.document. At minimum, theend-nodesend nodes require information to map a particular Bell pair to the qubit in their local memory that is part of this entangled pair.</t> </section> </section> </section> <sectiontitle="Architecturenumbered="true" toc="default"> <name>Architecture of aquantum internet">Quantum Internet</name> <t>It is evident from the previous sections that the fundamental service provided by a quantum network significantly differs from that of a classical network. Therefore, it is not surprising that the architecture of a quantum internet will itself be very different from that of the classical Internet.</t> <sectiontitle="Challenges">numbered="true" toc="default"> <name>Challenges</name> <t>This subsection covers the major fundamental challenges involved in building quantum networks. Here, we only describe the fundamental differences. Technological limitations are describedlater.</t> <t> <list style="numbers">in <xref target="phys-constraints"/>.</t> <ol spacing="normal" type="1"><li> <t>Bell pairs are not equivalent topayload carrying packets. <vspace blankLines="1" />packets that carry payload. </t> <t> In most classical networks, including Ethernet, Internet Protocol (IP), and Multi-Protocol Label Switching (MPLS) networks, user data is grouped into packets. In addition to the user data, each packet also contains a series of headerswhichthat contain the control information that lets routers and switches forward it towards its destination. Packets are the fundamental unit in a classical network.<vspace blankLines="1" /></t> <t> In a quantum network, the entangled pairs of qubits are the basic unit of networking. These qubits themselves do not carry any headers. Therefore, quantum networks will have to send all control information via separate classicalchannelschannels, which the repeaters will have to correlate with the qubits stored in their memory. Furthermore, unlike a classical packet, which is located at a single node, a Bell pair consists of two qubits distributed across twonodes which is unlike a classical packet which is located at a single node.nodes. This has a fundamental impact on how quantum networks will be managed and how protocols need to be designed. To make long-distance Bell pairs, the nodes may have to keep their qubits in their quantum memories and wait until control information is exchanged before proceeding with the next operation. This signalling will result in additionallatencylatency, which will depend on the distance between the nodes holding the two ends of the Bell pair. Error management, such as entanglement distillation, is a typical example of such control information exchange <xref target="Nagayama21"/>format="default"/> (see also <xref target="generations"/>).</t>format="default"/>).</t> </li> <li> <t>"Store and forward"vsand "store and swap" quantumnetworks. <vspace blankLines="1" />networks require different state management techniques. </t> <t> As described in <xref target="elg"/>,format="default"/>, quantum links provide Bell pairs that are undirected network resources, in contrast to directed frames of classical networks. This phenomenological distinction leads to architectural differences between quantum networks and classical networks. Quantum networks combine multiple elementary link Bell pairs together to create one end-to-end Bell pair, whereas classical networks deliver messages from one end to the other end hop by hop.<vspace blankLines="1" /></t> <t> Classical networks receive data on one interface, store it in local buffers, and then forward the data to another appropriate interface. Quantum networks store Bell pairs and then execute entanglement swapping instead of forwarding in the data plane. Such quantum networks are "store and swap" networks. In "store and swap" networks, we do not need to care about the order in which the Bell pairs weregeneratedgenerated, since they are undirected. However, whilst the ordering does not matter, it is very important that the right entangled pairs get swapped, and that the intermediate measurement outcomes (see <xref target="es"/>)format="default"/>) are signalled to and correlated with the correct qubits at the other nodes. Otherwise, the final end-to-end entangled pair will not be created between the expected end-points or will be in a different quantum state than expected. For example, rather than Alice receiving a qubit that is entangled with Bob's qubit, her qubit is entangled with Charlie's qubit. This distinction makes control algorithms and optimisation of quantum networks different from those for classicalones,networks, in the sense that swapping is stateful in contrast to stateless packet-by-packet forwarding. Notethat third generation quantum networks,that, as described in <xreftarget="elg" />,target="generations"/>, third-generation quantum networks will be able to support a "store and forward" architecture in addition to "store and swap".</t> </li> <li> <t>An entangled pair is only useful if the locations of both qubits are known.<vspace blankLines="1" /></t> <t> A classical network packet logically exists only at one location at any point in time. If a packet is modified in some way, whether headers or payload, this information does not need to be conveyed to anybody else in the network. The packet can be simply forwarded as before.<vspace blankLines="1" /></t> <t> In contrast, entanglement is a phenomenon in which two or more qubits exist in a physically distributed state. Operations on 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 must coordinate all its actions with the owner of the pair's other qubit. Therefore, the owner of any qubit that is part of an entangled pair must know the location of its counterpart. Location, in this context, need not be the explicit spatial location. A relevant pair identifier, a means of communication between the pair owners, and an association between the pair ID and the individual qubitsiswill be sufficient.</t> </li> <li> <t>Generating entanglement requires temporary state.<vspace blankLines="1" /></t> <t> Packet forwarding in a classical network is largely a stateless operation. When a packet is received, the router does a lookup in its forwarding table and sends the packet out of the appropriate output. There is no need to keep any memory of the packet any more.<vspace blankLines="1" /></t> <t> A quantum node must be able to make decisions about qubits that it receives and is holding in its memory. Since qubits do not carry headers, the receipt of an entangled pair conveys no control information based on which the repeater can make a decision. The relevant control information will arrive separately over a classical channel. This implies that a repeater must store temporarystatestate, as the control information and the qubit it pertains to will, in general, not arrive at the same time.</t></list> </t></li> </ol> </section> <sectiontitle="Classical communication">numbered="true" toc="default"> <name>Classical Communication</name> <t>In thisdraftdocument, we have already covered two different roles that classical communication mustperform:</t> <t> <list style="symbols"> <t>communicateperform the following:</t> <ul spacing="normal"> <li>Communicate classical bits of information as part of distributed protocols such as entanglement swapping andteleportation,</t> <t>communicateteleportation.</li> <li>Communicate control information within a network, includingbothbackground protocols such asroutingrouting, as well as signalling protocols to set up end-to-end entanglementgeneration.</t> </list> </t>generation.</li> </ul> <t>Classical communication is a crucial building block of any quantum network. All nodes in a quantum network are assumed to have classical connectivity with each other (within typical administrative domain limits). Therefore, quantum nodes will need to manage two data planes inparallel,parallel: a classicalonedata plane and a quantumone.data plane. Additionally, a node must be able to correlate information between the two planes so that the control information received on a classical channel can be applied to the qubits managed by the quantum data plane.</t> </section> <sectiontitle="Abstract modelnumbered="true" toc="default"> <name>Abstract Model of thenetwork"> <section title="The controlNetwork</name> <section numbered="true" toc="default"> <name>The Control Plane anddata planes">the Data Plane</name> <t>Control plane protocols for quantum networks will have many responsibilities similar to their classical counterparts, namely discovering the network topology, resource management, populating data plane tables, etc. Most of these protocols do not require the manipulation of quantum data and can operate simply by exchanging classical messages only. There may also be some control plane functionality that does require the handling of quantumdata, e.g. a quantum pingdata <xref target="I-D.irtf-qirg-quantum-internet-use-cases"/>.format="default"/>. As it is not clear if there is much benefit in defining a separate quantum control plane given the significant overlap in responsibilities with its classical counterpart, the question of whether there should be a separate quantum control plane is beyond the scope of this document.</t> <t>However, the data plane separation is much moredistinctdistinct, and there will be two data planes: a classical data plane and a quantum data plane. The classical data plane processes and forwards classical packets. The quantum data plane processes and swaps entangled pairs.Third generationThird-generation quantum networks may also forward qubits in addition to swapping Bell pairs.</t> <t>In addition to control plane messages, there will also be control information messages that operate at the granularity of individual entangled pairs, such as heralding messages used for elementary link generation (<xref target="elg"/>).format="default"/>). In terms of functionality, these messages are closer to classical packet headers than control planemessagesmessages, and thus we consider them to be part of the quantum data plane. Therefore, a quantum data plane also includes the exchange of classical control information at the granularity of individual qubits and entangled pairs.</t> </section> <sectiontitle="Elementsnumbered="true" toc="default"> <name>Elements of aquantum network">Quantum Network</name> <t>We have identified quantum repeaters as the core building block of a quantum network. However, a quantum repeater will have to do more than just entanglement swapping in a functional quantum network. Its key responsibilities willinclude:</t> <t> <list style="numbers"> <t>Creatinginclude the following:</t> <ol spacing="normal" type="1"><li>Creating link-local entanglement between neighbouringnodes.</t> <t>Extendingnodes.</li> <li>Extending entanglement from link-local pairs to long-range pairs through entanglementswapping.</t> <t>Performingswapping.</li> <li>Performing distillation to manage the fidelity of the producedpairs.</t> <t>Participatingpairs.</li> <li>Participating in the management of the network (routing,etc.).</t> </list> </t>etc.).</li> </ol> <t>Not all quantum repeaters in the network will be the same;herehere, we break them down further:</t><t> <list style="symbols"> <t>Quantum<dl spacing="normal"> <dt>Quantum routers (controllable quantumnodes) - Anodes):</dt><dd>A quantum router is a quantum repeater with a control plane that participates in the management of the network and will make decisions about which qubits to swap to generate the requested end-to-endpairs.</t> <t>Automatedpairs.</dd> <dt>Automated quantumnodes - Annodes:</dt><dd>An automated quantum node is adata plane onlydata-plane-only quantum repeater that does not participate in the network control plane. Since the no-cloning theorem precludes the use of amplification, long-range links will be established by chaining multiple such automated nodestogether.</t> <t>End-nodes - End-nodestogether.</dd> <dt>End nodes:</dt><dd>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 perform an entanglement swap (and thus are not necessarily quantum repeaters).End-nodesEnd nodes are also not required to have any quantummemorymemory, as certain quantum applications can be realised by having theend-nodeend node measure its qubit as soon as it isreceived.</t> <t>Non-quantum nodes - Notreceived.</dd> <dt>Non-quantum nodes:</dt><dd>Not all nodes in a quantum network need to have a quantum data plane. A non-quantum node is any device that can handle classical networktraffic.</t> </list> </t>traffic.</dd> </dl> <t>Additionally, we need to identify two kinds of links that will be used in a quantum network:</t><t> <list style="symbols"> <t>Quantum links - A<dl spacing="normal"> <dt>Quantum links:</dt><dd>A quantum link is a linkwhichthat can be used to generate an entangled pair between two directly connected quantum repeaters. This may include additional mid-point elements as described in <xref target="elg"/>.format="default"/>. It may also include a dedicated classical channel that is to be used solely for the purpose of coordinating the entanglement generation on this quantumlink.</t> <t>Classical links - Alink.</dd> <dt>Classical links:</dt><dd>A classical link is a link between any node in the network that is capable of carrying classical networktraffic.</t> </list> </t>traffic.</dd> </dl> <t>Note that passive elements, such as optical switches, do not destroy the quantum state. Therefore, it is possible to connect multiple quantum nodes with each other over an optical network and perform optical switching rather than routing via entanglement swapping at quantum routers. This does require coordination with the elementary link entanglement generationprocessprocess, and it still requires repeaters to overcome the short-distance limitations. However, this is a potentially feasible architecture for local area networks.</t> </section> <sectiontitle="Putting it all together">numbered="true" toc="default"> <name>Putting It All Together</name> <t>A two-hop path in a generic quantum network can be representedas:</t> <figure align="center">as follows:</t> <artworkalign="left"><![CDATA[align="left" name="" type="" alt=""><![CDATA[ +-----+ +-----+ | App |- - - - - - - - - -CC- - - - - - - - - -| App | +-----+ +------+ +-----+ | EN |------ CL ------| QR |------ CL ------| EN | | |------ QL ------| |------ QL ------| | +-----+ +------+ +-----+ App - user-level application EN -end-nodeEnd Node QL -quantum linkQuantum Link CL -classical linkClassical Link CC -classical channelClassical Channel (traverses one or more CLs) QR -quantum repeaterQuantum Repeater ]]></artwork></figure><t>An application (App) running on twoend-nodesEnd Nodes (ENs) attached to a network will at some point need the network to generate entangled pairs for its use. This may require negotiation between theend-nodesENs (possibly ahead of time), because they must both open a communication end-pointwhichthat the network can use to identify the two ends of the connection. The twoend-nodesENs use aclassical channelClassical Channel (CC) available in the network to achieve this goal.</t> <t>When the network receives a request to generate end-to-end entangledpairspairs, it uses theclassical communication linksClassical Links (CLs) to coordinate and claim the resources necessary to fulfill this request. This may be some combination of prior control information(e.g.(e.g., routing tables) and signalling protocols, but the details of how this is achieved are an active research question. A thought experiment on what this might look like be can be foundlater in this draftin <xref target="gedankenexperiment"/>.</t>format="default"/>.</t> <t>During or after the distribution of control information, the network performs the necessary quantumoperationsoperations, such as generating entanglement over individualquantum linksQuantum Links (QLs), performing entanglement swaps atquantum repeatersQuantum Repeaters (QRs), and further signalling to transmit the swap outcomes and other control information. Since Bell pairs do not carry any user data, some of these operations can be performed before the request isreceivedreceived, in anticipation of the demand.</t> <t>Note that here, "signalling" is used in a very broad sense and covers many different types of messaging necessary for entanglement generation control. For example, heralded entanglement generation requires very precise timing synchronisation between the neighbouringnodesnodes, and thus the triggering of entanglement generation and heralding may happen over its own, perhaps physicallyseparateseparate, CL, as was the case in the network stack demonstration described in <xref target="Pompili21.2"/>. Higher levelformat="default"/>. Higher-level signalling withless stringenttiming requirements(e.g.that are less stringent (e.g., control plane signalling) may then happen over its own CL.</t> <t>The entangled pair is delivered to the application once it is ready, together with the relevant pair identifier. However, being ready does not necessarily mean that all link pairs and entanglement swaps are complete, as some applications can start executing on an incomplete pair. In thiscasecase, the remaining entanglement swaps will propagate the actions across the network to the other end, sometimes necessitating fixup operations at theend node.</t>EN.</t> </section> </section> <sectiontitle="Physical constraints">anchor="phys-constraints" numbered="true" toc="default"> <name>Physical Constraints</name> <t>The model above has effectively abstracted away the particulars of the hardware implementation. However, certain physical constraints need to be considered in order to build a practical network. Some of these are fundamentalconstraintsconstraints, and no matter how much the technology improves, they will always need to be addressed. Others are artifacts of the early stages of a new technology. Here, we consider a highly abstract scenario and refer to <xreftarget="Wehner18"/>target="Wehner18" format="default"/> for pointers to the physics literature.</t> <sectiontitle="Memory lifetimes">numbered="true" toc="default"> <name>Memory Lifetimes</name> <t>In addition to discrete operations being imperfect, storing a qubit in memory is also highly non-trivial. The main difficulty in achieving persistent storage is that it is extremely challenging to isolate a quantum system from the environment. The environment introduces an uncontrollable source of noise into thesystemsystem, which affects the fidelity of the state. This process is known as decoherence. Eventually, the state has to be discarded once its fidelity degrades too much.</t> <t>The memory lifetime depends on the particular physical setup, but the highest achievable values in quantum network hardwarecurrently areare, as of 2020, on the order of seconds <xref target="Abobeih18"/>format="default"/>, although a lifetime of a minute has also been demonstrated for qubits not connected to a quantum network <xref target="Bradley19"/> (as of 2020).format="default"/>. These values have increased tremendously over the lifetime of the different technologies and are bound to keep increasing. However, if quantum networks are to be realised in the near future, they need to be able to handle short memorylifetimes,lifetimes -- forexampleexample, by reducing latency on critical paths.</t> </section> <sectiontitle="Rates">numbered="true" toc="default"> <name>Rates</name> <t>Entanglement generation on a link between two connected nodes is not a very efficientprocessprocess, and it requires many attempts to succeed <xref target="Hensen15"/>format="default"/> <xref target="Dahlberg19"/>.format="default"/>. For example, the highest achievable rates of success between nitrogen-vacancy centernodes, whichnodes -- which, in addition to entanglement generation are also capable of storing and processing the resultingqubits,qubits -- are on the order of 10 Hz. Combined with short memorylifetimeslifetimes, this leads to very tight timing windows to build up network-wide connectivity.</t> <t>Other platforms have shown higher entanglement rates, but this usually comes at the cost of other hardware capabilities, such as no quantum memory and/or limited processing capabilities <xref target="Wei22"/>.format="default"/>. Nevertheless, the current rates are not sufficient for practical applications beyond simple experimental proofs of concept. However, they are expected to improve over time as quantum network technology evolves <xref target="Wei22"/>.</t>format="default"/>.</t> </section> <sectiontitle="Communication qubits">numbered="true" toc="default"> <name>Communication Qubits</name> <t>Most physical architectures capable of storing qubits are only able to generate entanglement using only a subset of available qubits called communication qubits <xref target="Dahlberg19"/>.format="default"/>. Once a Bell pair has been generated using a communication qubit, its state can be transferred into memory. This may impose additional limitations on the network. In particular, if a given node has only one communicationqubitqubit, it cannot simultaneously generate Bell pairs over two links. It must generate entanglement over the links one at a time.</t> </section> <sectiontitle="Homogeneity"> <t>Currentlynumbered="true" toc="default"> <name>Homogeneity</name> <t>At present, all existing quantum network implementations arehomogeneoushomogeneous, and they do not interface with each other. In general, it is very challenging to combine different quantum information processing technologies.</t> <t>There are many different physical hardware platforms for implementing quantum networking hardware. The different technologies differ in how they store and manipulate qubits in memory and how they generate entanglement across a link with their neighbours. For example, hardware based on optical elements and atomic ensembles <xref target="Sangouard11"/>format="default"/> is very efficient at generating entanglement at highrates,rates but provides limited processing capabilities once the entanglement is generated. On the other hand,nitrogen-vacancy basednitrogen-vacancy-based platforms <xref target="Hensen15"/>format="default"/> or trapped ion platforms <xref target="Moehring07"/> platformsformat="default"/> offer a much greater degree of control over thequbits,qubits but have a harder time generating entanglement at high rates.</t> <t>In order to overcome the weaknesses of the different platforms, coupling the different technologies will help to build fully functional networks. For example,end-nodesend nodes may be implemented using technology with good qubit processing capabilities to enable complex applications, but automated quantum nodes thatthatserve only to "repeat" along a linear chain, where the processing logic is much simpler, can be implemented with technologies that sacrifice processing capabilities for higher entanglement rates at long distances <xref target="Askarani21"/>.</t>format="default"/>.</t> <t>This point is further exacerbated by the fact that quantum computers(i.e. end-nodes(i.e., end nodes in a quantum network) are often based on different hardware platforms than quantumrepeatersrepeaters, thus requiring a coupling (transduction) between the two. This is especially true for quantum computers based on superconductingtechnologytechnology, which are challenging to connect to optical networks. However, even trapped ion quantum computers, whichismake up a platform that has shown promise for quantum networking, will still need to connect to other platforms that are better at creating entanglement at high rates over long distances (hundreds ofkms).</t>kilometres).</t> </section> </section> </section> <sectiontitle="Architectural principles">numbered="true" toc="default"> <name>Architectural Principles</name> <t>Given that the most practical way of realising quantum network connectivity is using Bell pair andentanglement swappingentanglement-swapping repeater technology, what sort of principles should guide us in assembling such networks such that they are functional, robust, efficient,andand, most importantly,do theywill work? Furthermore, how do we design networks so that they work under the constraints imposed by the hardware availabletoday,today but do not impose unnecessary burdens on future technology?</t> <t>As quantum networking is a completely new technology that is likely to see many iterations over its lifetime, thisdraftdocument must not serve as a definitive set ofrules,rules but merely as a general set of recommended guidelines for the first generations of quantum networks based on principles and observations made by the community. The benefit of having acommunity builtcommunity-built document at this early stage is that expertise in both quantum information and network architecture is needed in order to successfully build a quantum internet.</t> <sectiontitle="Goalsanchor="goals" numbered="true" toc="default"> <name>Goals of aquantum internet">Quantum Internet</name> <t>When outlining any set ofprinciplesprinciples, we must ask ourselves what goalsdowe want toachieveachieve, as inevitably trade-offs must be made.SoSo, what sort of goals should drive a quantum network architecture? The following list has been inspired by the history of computernetworkingnetworking, and thus it is inevitably very similar to one that could be produced for the classical Internet <xref target="Clark88"/>.format="default"/>. However, whilst the goals may besimilarsimilar, the challenges involved are often fundamentally different. The list will also most likely evolve with time and the needs of its users.</t><t> <list style="numbers"><ol spacing="normal" type="1"><li> <t>Support distributed quantumapplications <vspace blankLines="1" />applications. </t> <t> This goal seems trivially obvious, but it makes a subtle, butimportantimportant, pointwhichthat highlights a key difference between quantum and classical networks. Ultimately, quantum data transmission is not the goal of a quantum network--- it is only one possible component ofmore advancedquantum application protocols that are more advanced <xref target="Wehner18"/>.format="default"/>. Whilst transmission certainly could be used as a building block for all quantum applications, it is not the most basic one possible. For example, entanglement-based QKD, the mostwell knownwell-known quantum application protocol, only relies on the stronger-than-classical correlations and inherent secrecy of entangled Bell pairs and does not have to transmit arbitrary quantum states <xref target="Ekert91"/>. <vspace blankLines="1" />format="default"/>. </t> <t> The primary purpose of a quantum internet is to support distributed quantum applicationprotocolsprotocols, and it is of utmost importance that they can run well and efficiently. Thus, it is important to develop performance metrics meaningful toapplicationapplications to drive the development of quantum network protocols. For example, the Bell pair generation rate is meaningless if one does not also consider their fidelity. It is generally much easier to generate pairs of lower fidelity, but quantum applications may have to make multiplere-attemptsreattempts or even abort if the fidelity is too low. A review of the requirements for different known quantum applications can be found in <xref target="Wehner18"/>format="default"/>, and an overview ofuse-casesuse cases can be found in <xref target="I-D.irtf-qirg-quantum-internet-use-cases"/>.</t>format="default"/>.</t> </li> <li> <t>Support tomorrow's distributed quantumapplications <vspace blankLines="1" />applications. </t> <t> The only principle of the Internet that should survive indefinitely is the principle of constant change <xref target="RFC1958"/>.format="default"/>. Technical change iscontinuouscontinuous, and the size and capabilities of the quantum internet will change by orders of magnitude. Therefore, it is an explicit goal that a quantum internet architecture be able to embrace this change. We have the benefit of having been witness to the evolution of the classical Internet over severaldecadesdecades, and we have seen what worked and what did not. It is vital for a quantum internet to avoid the need for flag days(e.g.(e.g., NCP to TCP/IP) or upgrades that take decades to roll out(e.g.(e.g., IPv4 to IPv6).<vspace blankLines="1" /></t> <t> Therefore, it is important that any proposed architecture forgeneral purposegeneral-purpose quantum repeater networks can integrate new devices and solutions as they become available. The architecture should not be constrained due to considerations for early-stage hardware and applications. For example, it is already possible to run QKD efficiently onmetropolitan scalesmetropolitan-scale networks, and such networks are already commercially available. However, they are not based on quantum repeaters and thus will not be able to easily transition to applications that are moresophisticated applications.</t>sophisticated.</t> </li> <li> <t>Supportheterogeneity <vspace blankLines="1" />heterogeneity. </t> <t> There are multiple proposals for realising practical quantum repeaterhardwarehardware, and they all have their advantages and disadvantages. Some may offer higher Bell pair generation rates on individual links at the cost ofmore difficultentanglement swapoperations.operations that are more difficult. Other platforms may be good allaround,around but are more difficult to build.<vspace blankLines="1" /></t> <t> In addition to physical boundaries, there may be distinctions in how errors are managed (<xref target="generations"/>).format="default"/>). Thesedifferencedifferences will affect the content and semantics of messages that cross these boundaries --bothfor both connection setup and real-time operation.<vspace blankLines="1" /></t> <t> The optimal network configuration will likely leverage the advantages of multiple platforms to optimise the provided service. Therefore, it is an explicit goal to incorporate varied hardware and technology support from the beginning.</t> </li> <li> <t>Ensure security at the networklevel <vspace blankLines="1" />level. </t> <t> The question of security in quantum networks is just as critical as it is in the classical Internet, especially since enhanced security offered by quantum entanglement is one of the key driving factors.<vspace blankLines="1" /></t> <t> Fortunately, from an application's point of view, as long as the underlying implementation corresponds to (or sufficiently approximates) theoretical models of quantum cryptography, quantum cryptographic protocols do not need the network to provide any guarantees about the confidentiality or integrity of the transmitted qubits or the generated entanglement (though they may impose requirements on the classical channel,e.ge.g., to be authenticated <xref target="Wang21"/>).format="default"/>). Instead, applications will leverage the classical networks to establish the end-to-end security of the results obtained from the processing of entangled qubits. However, it is important to note that whilst classical networks are necessary to establish these end-to-end guarantees, the security relies on the properties of quantum entanglement. For example, QKD uses classical information reconciliation <xreftarget= "Tang19" />target="Tang19" format="default"/> for error correction and privacy amplification <xreftarget= "Elkouss11" />target="Elkouss11" format="default"/> for generating the final secure key, but the raw bits that are fed into these protocols must come from measuring entangled qubits <xref target="Ekert91"/>.format="default"/>. In another application, secure delegated quantum computing, the client hides its computation from the server by sending qubits to the server and then requestingit(in a classical message)tothat the server measure them in an encoded basis. The client then decodes the results it receives from the server to obtain the result of the computation <xreftarget= "Broadbent10" />.target="Broadbent10" format="default"/>. Once again, whilst a classical network is used to achieve the goal of secure computation, the remote computation is strictly quantum.<vspace blankLines="1" /></t> <t> Nevertheless, whilst applications can ensure their own end-to-end security, network protocols themselves should be security aware in order to protect the network itself and limit disruption. Whilst the applications remainsecuresecure, they are not necessarily operational or as efficient in the presence of an attacker. For example, if an attacker can measure every qubit between two parties trying to establish a key using QKD, no secret key can be generated. Security concerns in quantum networks are described in more detail in <xref target="Satoh17"/>format="default"/> and <xref target="Satoh20"/>.</t>format="default"/>.</t> </li> <li> <t>Make them easy tomonitor <vspace blankLines="1" />monitor. </t> <t> In order to manage, evaluate the performance of, or debug anetworknetwork, it is necessary to have the ability to monitor the network while ensuring that there will be mechanisms in place to protect the confidentiality and integrity of the devices connected to it. Quantum networks bring new challenges in thisareaarea, so it should be a goal of a quantum network architecture to make this task easy.<vspace blankLines="1" /></t> <t> The fundamental unit of quantum information, the qubit, cannot be activelymonitoredmonitored, as any readout irreversibly destroys its contents. One of the implications of this fact is that measuring an individual pair's fidelity is impossible. Fidelity is meaningful only as a statistical quantitywhichthat requirestheconstant monitoringand the sacrificeof generated Bell pairs, achieved by sacrificing some Bell pairs for use in tomography or other methods.<vspace blankLines="1" /></t> <t> Furthermore, given one end of an entangled pair, it is impossible to tell where the other qubit is without any additional classical metadata. It is impossible to extract this information from the qubits themselves. This implies that tracking entangled pairs necessitates some exchange of classical information. This information might include (i) a reference to the entangled pair that allows distributed applications to coordinate actions on qubits of the samepair,pair and (ii) the two bits from each entanglement swap necessary to identify the final state of the Bell pair (<xref target="es"/>).</t>format="default"/>).</t> </li> <li> <t>Ensure availability andresilience <vspace blankLines="1" />resilience. </t> <t> Any practical and usable network, classical or quantum, must be able to continue to operate despite losses andfailures,failures and be robust to malicious actors trying to disable connectivity.What differs inA difference between quantumnetworks as compared toand classical networksin this regardis thatwe now havequantum networks are composed of two types of data planes (quantum and classical) and two types of channelsto worry about: a quantum(quantum anda classical one.classical) that must be considered. Therefore, availability and resilience will most likely require a more advanced treatment than they do in classical networks.</t></list> </t></li> </ol> <t>Note that privacy, whilst related to security, is not listed as an explicit goal, because the privacy benefits will depend on the use case. For example, QKD only provides increased security for the distribution of symmetric keys <xref target="Bennett14"/>format="default"/> <xref target="Ekert91"/>.format="default"/>. The handling, manipulation, sharing, encryption, and decryption of data will remain entirelyclassicalclassical, limiting the benefits to privacy that can be gained from using a quantum network. On the other hand, there are applications like blind quantumcomputationcomputation, which provides the user with the ability to execute a quantum computation on a remote server without the server knowing what the computation was or its input and output <xref target="Fitzsimons17"/>.format="default"/>. Therefore, privacy must be considered on a per-application basis. An overview of quantum network use cases can be found in <xref target="I-D.irtf-qirg-quantum-internet-use-cases"/>.</t>format="default"/>.</t> </section> <sectiontitle="The principlesnumbered="true" toc="default"> <name>The Principles of aquantum internet">Quantum Internet</name> <t>The principles support thegoals,goals but are not goals themselves. The goals define what we want tobuildbuild, and the principles provide a guidelineinfor how we might achieve this. The goals will also be the foundation for defining any metric of success for a network architecture, whereas the principles in themselves do not distinguish between success and failure. For more information about design considerations for quantumnetworksnetworks, see <xref target="VanMeter13.1"/>format="default"/> and <xref target="Dahlberg19"/>.</t> <t> <list style="numbers">format="default"/>.</t> <ol spacing="normal" type="1"><li> <t>Entanglement is the fundamentalservice <vspace blankLines="1" />service. </t> <t> The key service that a quantum network provides is the distribution of entanglement between the nodes in a network. All distributed quantum applications are built on top of this key resource. Applications such as clustered quantum computing, distributed quantum computing, distributed quantum sensing networks, and certain kinds of quantum secure networks all consume quantum entanglement as a resource. Some applications(e.g. quantum key distribution)(e.g., QKD) simply measure the entangled qubits to obtain a shared secret key <xref target="QKD"/>.format="default"/>. Other applications(e.g.(e.g., distributed quantum computing) buildmore complexabstractions and operations that are more complex on the entangled qubits, e.g., distributed CNOT gates <xref target="DistCNOT"/>format="default"/> or teleportation of arbitrary qubit states <xref target="Teleportation"/>. <vspace blankLines="1" />format="default"/>. </t> <t> A quantum network may also distribute multipartite entangled states (entangled states of three or more qubits) <xref target="Meignant19"/>format="default"/>, which are useful for applications such as conference key agreement <xref target="Murta20"/>,format="default"/>, distributed quantum computing <xref target="Cirac99"/>,format="default"/>, secret sharing <xref target="Qin17"/>,format="default"/>, and clock synchronisation <xref target="Komar14"/>. Thoughformat="default"/>, though itwasis worth noting that multipartite entangled states can also be constructed from multiple entangled pairs distributed between theend-nodes.</t>end nodes.</t> </li> <li> <t>BellPairspairs areindistinguishable <vspace blankLines="1" />indistinguishable. </t> <t> Any two BellPairspairs between the same two nodes are indistinguishable for the purposes of anapplicationapplication, provided they both satisfy its required fidelity threshold. This observation is likely to be key in enabling a more optimal allocation of resources in a network,e.g.e.g., for the purposes of provisioning resources to meet application demand. However, the qubits that make up the pair themselves are notindistinguishableindistinguishable, and the two nodes operating on a pair must coordinate to make sure they are operating on qubits that belong to the same Bell pair.</t> </li> <li> <t>Fidelity is part of theservice <vspace blankLines="1" />service. </t> <t> In addition to being able to deliver Bell pairs to the communication end-points, the BellPairspairs must be of sufficient fidelity. Unlike in classicalnetworksnetworks, where most errors are effectively eliminated before reaching the application, many quantum applications only need imperfect entanglement to function. However, quantum applications will generally have a threshold for Bell pair fidelity below which they are no longer able to operate. Different applications will have different requirements for what fidelity they can work with. It is the network's responsibility to balance the resource usage with respect to the applications' requirements. It may be that it is cheaper for the network to providelower fidelitylower-fidelity pairs that are just above the threshold required by the application than it is to guaranteehigh fidelityhigh-fidelity pairs to all applications regardless of their requirements.</t> </li> <li> <t>Time is an expensiveresource <vspace blankLines="1" />resource. </t> <t> Time is not the only resource that is in short supply(memory, and communication(communication qubits and memory are as well), but ultimately it is the lifetime of quantum memories that imposes some of the most difficult conditions for operating an extended network of quantum nodes. Current hardware has low rates of Bell pair generation, short memory lifetimes, and access to a limited number of communication qubits. All these factors combined mean that even 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 application's fidelity threshold. Therefore, managing the idle time of qubits holding live quantum states should be donecarefully. Ideallycarefully -- ideally by minimising the idle time, but potentially also by moving the quantum state for temporary storage to a quantum memory with a longer lifetime.</t> </li> <li> <t>Be flexible with regards to capabilities andlimitations <vspace blankLines="1" />limitations. </t> <t> This goal encompasses two importantpoints. First,points:</t> <ul spacing="normal"> <li>First, the architecture should be able to function under the physical constraints imposed by thecurrent generationcurrent-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 pairsunusable. <vspace blankLines="1" /> Second,unusable.</li> <li>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 willimproveimprove, and redeploying a technology is extremelychallenging.</t> </list> </t>challenging.</li> </ul> </li> </ol> </section> </section> <sectiontitle="A thought experiment inspiredanchor="gedankenexperiment" numbered="true" toc="default"> <name>A Thought Experiment Inspired byclassical networks" anchor="gedankenexperiment">Classical Networks</name> <t>To conclude, we discuss a plausible quantum network architecture inspired by MPLS. This is not an architectureproposal,proposal but rather a thought experiment to give the reader an idea of what components are necessary for a functional quantum network. We use classical MPLS as abasisbasis, as it is well known and understood in the networking community.</t> <t>Creating end-to-end Bell pairs between remote end-points is a stateful distributed task that requires a lot ofa-prioria priori coordination. Therefore, a connection-oriented approach seems the most natural for quantum networks. In connection-oriented quantum networks, when two quantum application end-points wish to start creating end-to-end Bell pairs, they must first create aquantum virtual circuitQuantum Virtual Circuit (QVC). As an analogy, in MPLSnetworksnetworks, end-points must establish alabel switched pathLabel Switched Path (LSP) before exchanging traffic. Connection-oriented quantum networks may also support virtual circuits with multiple end-points for creating multipartite entanglement. As an analogy, MPLS networks have the concept ofmulti-pointmultipoint LSPs for multicast.</t> <t>When a quantum application creates aquantum virtual circuit,QVC, it can indicatequalityQuality ofserviceService (QoS) parameters such as the required capacity in end-to-end Bellpairs per secondPairs Per Second (BPPS) and the required fidelity of the Bell pairs. As an analogy, in MPLSnetworksnetworks, applications specify the required bandwidth inbits per secondBits Per Second (BPS) and other constraints when they create a new LSP.</t> <t>Different applications will have different QoS requirements. For example, applications such asQKD,QKD that don't need to process the entangledqubitsqubits, and only need measure them and store the resulting outcome, may require a large volume ofentanglement,entanglement but will be tolerant of delay and jitter for individual pairs. On the other hand, distributed/cloud quantum computing applications may need fewer entangledpairs,pairs butinstead,instead may need all of them to be generated in one go so that they can all be processedalltogether before any of them decohere.</t> <t>Quantum networks need a routing function to compute the optimal path(i.e.(i.e., the best sequence of routers and links) for each newquantum virtual circuit.QVC. The routing function may becentralizedcentralised or distributed. In the latter case, the quantum network needs a distributed routing protocol. As an analogy, classical networks use routing protocols such asopen shortest path firstOpen Shortest Path First (OSPF) andintermediate-systemIntermediate System tointermediate systemIntermediate System (IS-IS). However, note that the definition of"shortest-path"/"least-cost""shortest path" / "least cost" may be different in a quantum network to account for its non-classical features, such as fidelity <xref target="VanMeter13.2"/>.</t>format="default"/>.</t> <t>Given the very scarce availability of resources in early quantum networks, atraffic engineeringTraffic Engineering (TE) function is likely to be beneficial. Withouttraffic engineering, quantum virtual circuitsTE, QVCs always use the shortest path. In this case, the quantum network cannot guarantee that each quantum end-point will get its Bell pairs at the required rate or fidelity. This is analogous to "best effort" service in classical networks.</t> <t>Withtraffic engineering, quantum virtual circuitsTE, QVCs choose a path that is guaranteed to have the requested resources(e.g.(e.g., bandwidth in BPPS) available, taking into account the capacity of the routers and links and also taking into account the resources already consumed by other virtual circuits. As an analogy, both OSPF and IS-IS havetraffic engineering (TE)TE extensions to keep track of used and availableresources,resources and can useconstrained shortest path firstConstrained Shortest Path First (CSPF) to take resource availability and other constraints into account when computing the optimal path.</t> <t>The use oftraffic engineeringTE implies the use ofcall admission controlCall Admission Control (CAC): the network denies any virtual circuits for which it cannot guarantee the requested quality of servicea-priori. Or alternatively,a priori. Alternatively, the networkpre-empts lower prioritypreempts lower-priority circuits to make room forthea newone.</t>circuit.</t> <t>Quantum networks need asignalingsignalling function: once the path for aquantum virtual circuitQVC has been computed,signalingsignalling is used to install the "forwarding rules" into the data plane of each quantum router on the path. Thesignalingsignalling may be distributed, analogous to theresource reservation protocolResource Reservation Protocol (RSVP) in MPLS.OrOr, thesignalingsignalling may becentralized,centralised, similar to OpenFlow.</t> <t>Quantum networks need an abstraction of the hardware for specifying the forwarding rules. This allows us tode-coupledecouple the control plane (routing andsignaling)signalling) from the data plane (actual creation of Bell pairs). The forwarding rules are specified using abstract building blocks such as "creating local Bell pairs", "swapping Bell pairs", or "distillation of Bell pairs". As an analogy, classical networks use abstractions that are based on match conditions(e.g.(e.g., looking up header fields in tables) and actions(e.g.(e.g., modifying fields or forwarding a packet to a specific interface). Thedata-planedata plane abstractions in quantum networks will be very different from those in classical networks due to the fundamental differences in technology and the stateful nature of quantum networks. In fact, choosing the right abstractions will be one of the biggest challenges when designing interoperable quantum network protocols.</t> <t>In quantum networks, control plane traffic (routing andsignalingsignalling messages) is exchanged over a classical channel, whereas data plane traffic (the actual Bell pair qubits) is exchanged over a separate quantum channel. This is in contrast to most classical networks, where control plane traffic and data plane traffic share the same channel and where a single packet contains both user fields and header fields. There is, however, a classical analogy to the way quantum networkswork. Generalizedwork: generalised MPLS (GMPLS) networks use separate channels for control plane traffic and data plane traffic. Furthermore, GMPLS networks support data planes where there is no such thing as data plane headers(e.g. DWDM or TDM(e.g., Dense Wavelength Division Multiplexing (DWDM) or Time-Division Multiplexing (TDM) networks).</t> </section> <section anchor="Security"title="Security Considerations">numbered="true" toc="default"> <name>Security Considerations</name> <t>Security is listed as an explicit goal for thearchitecture andarchitecture; this issue is addressed inthe section on goals.<xref target="goals"/>. 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If you use the PI option, xml2rfc will, by default, try to find included files in the same directory as the including file. You can also define the XML_LIBRARY environment variable with a value containing a set of directories to search. 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<contact fullname="Axel Dahlberg"/>, <contact fullname="Mathias van den Bossche"/>, <contact fullname="Patrick Gelard"/>, <contact fullname="Chonggang Wang"/>, <contact fullname="Scott Fluhrer"/>, <contact fullname="Joey Salazar"/>, <contact fullname="Joseph Touch"/>, and the rest of the QIRG community as a whole for their very useful reviews and comments on this document.</t> <t>WK and SW acknowledge funding received from the EU Flagship on Quantum Technologies, Quantum Internet Alliance (No. 820445).</t> <t>rdv acknowledges support by the Air Force Office of Scientific Research under award number FA2386-19-1-4038.</t> </section> </back> </rfc>