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Checking references for intended status: Informational ---------------------------------------------------------------------------- == Outdated reference: A later version (-19) exists of draft-irtf-qirg-quantum-internet-use-cases-05 Summary: 0 errors (**), 0 flaws (~~), 2 warnings (==), 1 comment (--). Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 Quantum Internet Research Group W. Kozlowski 3 Internet-Draft S. Wehner 4 Intended status: Informational QuTech 5 Expires: December 6, 2021 R. Van Meter 6 Keio University 7 B. Rijsman 8 Individual 9 A. S. Cacciapuoti 10 M. Caleffi 11 University of Naples Federico II 12 S. Nagayama 13 Mercari, Inc. 14 June 4, 2021 16 Architectural Principles for a Quantum Internet 17 draft-irtf-qirg-principles-07 19 Abstract 21 The vision of a quantum internet is to fundamentally enhance Internet 22 technology by enabling quantum communication between any two points 23 on Earth. To achieve this goal, a quantum network stack should be 24 built from the ground up to account for the fundamentally new 25 properties of quantum entanglement. The first realisations of 26 quantum entanglement networks are imminent, but there is no practical 27 proposal for how to organise, utilise, and manage such networks. In 28 this memo, we attempt to lay down the framework and introduce some 29 basic architectural principles for a quantum internet. This is 30 intended for general guidance and general interest, but also to 31 provide a foundation for discussion between physicists and network 32 specialists. This document is a product of the Quantum Internet 33 Research Group (QIRG). 35 Status of This Memo 37 This Internet-Draft is submitted in full conformance with the 38 provisions of BCP 78 and BCP 79. 40 Internet-Drafts are working documents of the Internet Engineering 41 Task Force (IETF). Note that other groups may also distribute 42 working documents as Internet-Drafts. The list of current Internet- 43 Drafts is at https://datatracker.ietf.org/drafts/current/. 45 Internet-Drafts are draft documents valid for a maximum of six months 46 and may be updated, replaced, or obsoleted by other documents at any 47 time. It is inappropriate to use Internet-Drafts as reference 48 material or to cite them other than as "work in progress." 49 This Internet-Draft will expire on December 6, 2021. 51 Copyright Notice 53 Copyright (c) 2021 IETF Trust and the persons identified as the 54 document authors. All rights reserved. 56 This document is subject to BCP 78 and the IETF Trust's Legal 57 Provisions Relating to IETF Documents 58 (https://trustee.ietf.org/license-info) in effect on the date of 59 publication of this document. Please review these documents 60 carefully, as they describe your rights and restrictions with respect 61 to this document. Code Components extracted from this document must 62 include Simplified BSD License text as described in Section 4.e of 63 the Trust Legal Provisions and are provided without warranty as 64 described in the Simplified BSD License. 66 Table of Contents 68 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 69 2. Quantum information . . . . . . . . . . . . . . . . . . . . . 4 70 2.1. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 4 71 2.2. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 5 72 3. Entanglement as the fundamental resource . . . . . . . . . . 6 73 4. Achieving quantum connectivity . . . . . . . . . . . . . . . 8 74 4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 8 75 4.1.1. The measurement problem . . . . . . . . . . . . . . . 8 76 4.1.2. No-cloning theorem . . . . . . . . . . . . . . . . . 8 77 4.1.3. Fidelity . . . . . . . . . . . . . . . . . . . . . . 9 78 4.1.4. Inadequacy of direct transmission . . . . . . . . . . 9 79 4.2. Bell pairs . . . . . . . . . . . . . . . . . . . . . . . 10 80 4.3. Teleportation . . . . . . . . . . . . . . . . . . . . . . 10 81 4.4. The life cycle of entanglement . . . . . . . . . . . . . 11 82 4.4.1. Elementary link generation . . . . . . . . . . . . . 11 83 4.4.2. Entanglement swapping . . . . . . . . . . . . . . . . 13 84 4.4.3. Error Management . . . . . . . . . . . . . . . . . . 14 85 4.4.4. Delivery . . . . . . . . . . . . . . . . . . . . . . 16 86 5. Architecture of a quantum internet . . . . . . . . . . . . . 17 87 5.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 17 88 5.2. Classical communication . . . . . . . . . . . . . . . . . 19 89 5.3. Abstract model of the network . . . . . . . . . . . . . . 19 90 5.3.1. The control and data planes . . . . . . . . . . . . . 19 91 5.3.2. Elements of a quantum network . . . . . . . . . . . . 20 92 5.3.3. Putting it all together . . . . . . . . . . . . . . . 21 93 5.4. Network boundaries . . . . . . . . . . . . . . . . . . . 22 94 5.4.1. Boundaries between different physical architectures . 22 95 5.4.2. Boundaries between different administrative regions . 23 96 5.4.3. Boundaries between different error management schemes 23 98 5.5. Physical constraints . . . . . . . . . . . . . . . . . . 23 99 5.5.1. Memory lifetimes . . . . . . . . . . . . . . . . . . 23 100 5.5.2. Rates . . . . . . . . . . . . . . . . . . . . . . . . 24 101 5.5.3. Communication qubits . . . . . . . . . . . . . . . . 24 102 5.5.4. Homogeneity . . . . . . . . . . . . . . . . . . . . . 24 103 6. Architectural principles . . . . . . . . . . . . . . . . . . 24 104 6.1. Goals of a quantum internet . . . . . . . . . . . . . . . 25 105 6.2. The principles of a quantum internet . . . . . . . . . . 28 106 7. A thought experiment inspired by classical networks . . . . . 29 107 8. Security Considerations . . . . . . . . . . . . . . . . . . . 32 108 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 32 109 10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 32 110 11. Informative References . . . . . . . . . . . . . . . . . . . 32 111 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 38 113 1. Introduction 115 Quantum networks are distributed systems of quantum devices that 116 utilise fundamental quantum mechanical phenomena such as 117 superposition, entanglement, and quantum measurement to achieve 118 capabilities beyond what is possible with non-quantum (classical) 119 networks [Kimble08]. Depending on the stage of a quantum network 120 [Wehner18] such devices may range from simple photonic devices 121 capable of preparing and measuring only one quantum bit (qubit) at a 122 time all the way to large-scale quantum computers of the future. A 123 quantum network is not meant to replace classical networks, but 124 rather form an overall hybrid classical-quantum network supporting 125 new capabilities which are otherwise impossible to realise 126 [VanMeterBook]. 128 This new networking paradigm offers promise for a range of new 129 applications such as quantum cryptography [Bennett14] [Ekert91], 130 distributed quantum computation [Crepeau02], secure quantum computing 131 in the cloud [Fitzsimons17], quantum-enhanced measurement networks 132 [Giovanetti04], or higher-precision, long-baseline telescopes 133 [Gottesman12]. The field of quantum communication has been a subject 134 of active research for many years and the most well-known application 135 of quantum communication, quantum key distribution (QKD) for secure 136 communications, has already been deployed at short (roughly 100km) 137 distances [Elliott03] [Peev09] [Aguado19]. 139 Fully quantum networks capable of transmitting and managing entangled 140 quantum states in order to send, receive, and manipulate distributed 141 quantum information are now imminent [Castelvecchi18] [Wehner18]. 142 Whilst a lot of effort has gone into physically realising and 143 connecting such devices [Hensen15], and making improvements to their 144 speed and error tolerance, there are no worked out proposals for how 145 to run these networks. To draw an analogy with a classical network, 146 we are at a stage where we can start to physically connect our 147 devices and send data, but all sending, receiving, buffer management, 148 connection synchronisation, and so on, must be managed by the 149 application itself at a level below conventional assembly language, 150 where no common interfaces yet exist. Furthermore, whilst physical 151 mechanisms for transmitting quantum states exist, there are no robust 152 protocols for managing such transmissions. 154 This document, the result of the Quantum Internet Research Group 155 (QIRG), introduces the subject matter for quantum networks and 156 presents general guidelines for the design and construction of such 157 networks. Overall, it is intended as an introduction to the subject 158 for network engineers and researchers. It should not be considered 159 as a conclusive statement on how quantum network should or will be 160 implemented. This document was discussed on the QIRG mailing list 161 and several IETF meetings and represents the consensus of the QIRG 162 members, both of experts in the subject matter (from the quantum as 163 well networking domain) as well as newcomers who are the target 164 audience. 166 2. Quantum information 168 In order to understand the framework for quantum networking, a basic 169 understanding of quantum information is necessary. The following 170 sections aim to introduce the bare minimum necessary to understand 171 the principles of operation of a quantum network. This exposition 172 was written with a classical networking audience in mind. It is 173 assumed that the reader has never before been exposed to any quantum 174 physics. We refer to e.g. [SutorBook] [NielsenChuang] for an in- 175 depth introduction to quantum information. 177 2.1. Qubit 179 The differences between quantum computation and classical computation 180 begin at the bit-level. A classical computer operates on the binary 181 alphabet { 0, 1 }. A quantum bit, called a qubit, exists over the 182 same binary space, but unlike the classical bit, it can exist in a 183 superposition of the two possibilities: 185 a |0> + b |1>, 187 where |X> is Dirac's ket notation for a quantum state, here the 188 binary 0 and 1, and the coefficients a and b are complex numbers 189 called probability amplitudes. Physically, such a state can be 190 realised using a variety of different technologies such as electron 191 spin, photon polarisation, atomic energy levels, and so on. 193 Upon measurement, the qubit loses its superposition and irreversibly 194 collapses into one of the two basis states, either |0> or |1>. Which 195 of the two states it ends up in may not be deterministic, but can be 196 determined from the readout of the measurement. The measurement 197 result is a classical bit, 0 or 1, corresponding to |0> and |1> 198 respectively. The probability of measuring the state in the |0> 199 state is |a|^2 and similarly the probability of measuring the state 200 in the |1> state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness 201 is not due to our ignorance of the underlying mechanisms, but rather 202 is a fundamental feature of a quantum mechanical system [Aspect81]. 204 The superposition property plays an important role in fundamental 205 gate operations on qubits. Since a qubit can exist in a 206 superposition of its basis states, the elementary quantum gates are 207 able to act on all states of the superposition at the same time. For 208 example, consider the NOT gate: 210 NOT (a |0> + b |1>) -> a |1> + b |0>. 212 2.2. Multiple qubits 214 When multiple qubits are combined in a single quantum state the space 215 of possible states grows exponentially and all these states can 216 coexist in a superposition. For example, the general form of a two- 217 qubit register is 219 a |00> + b |01> + c |10> + d |11> 221 where the coefficients have the same probability amplitude 222 interpretation as for the single qubit state. Each state represents 223 a possible outcome of a measurement of the two-qubit register. For 224 example, |01> denotes a state in which the first qubit is in the 225 state |0> and the second is in the state |1>. 227 Performing single qubit gates affects the relevant qubit in each of 228 the superposition states. Similarly, two-qubit gates also act on all 229 the relevant superposition states, but their outcome is far more 230 interesting. 232 Consider a two-qubit register where the first qubit is in the 233 superposed state (|0> + |1>)/sqrt(2) and the other is in the 234 state |0>. This combined state can be written as: 236 (|0> + |1>)/sqrt(2) x |0> = (|00> + |10>)/sqrt(2), 238 where x denotes a tensor product (the mathematical mechanism for 239 combining quantum states together). Let us now consider the two- 240 qubit controlled-NOT, or CNOT, gate. The CNOT gate takes as input 241 two qubits, a control and target, and applies the NOT gate to the 242 target if the control qubit is set. The truth table looks like 244 +----+-----+ 245 | IN | OUT | 246 +----+-----+ 247 | 00 | 00 | 248 | 01 | 01 | 249 | 10 | 11 | 250 | 11 | 10 | 251 +----+-----+ 253 Now, consider performing a CNOT gate on the state with the first 254 qubit being the control. We apply a two-qubit gate on all the 255 superposition states: 257 CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2). 259 What is so interesting about this two-qubit gate operation? The 260 final state is *entangled*. There is no possible way of representing 261 that quantum state as a product of two individual qubits; they are no 262 longer independent and the behaviour of either qubit cannot be fully 263 described without accounting for the other qubit. The states of the 264 two individual qubits are now correlated beyond what is possible to 265 achieve classically. Neither qubit is in a definite |0> or |1> 266 state, but if we perform a measurement on either one, the outcome of 267 the partner qubit will *always* yield the exact same outcome. The 268 final state, whether it's |00> or |11>, is fundamentally random as 269 before, but the states of the two qubits following a measurement will 270 always be identical. 272 Once a measurement is performed, the two qubits are once again 273 independent. The final state is either |00> or |11> and both of 274 these states can be trivially decomposed into a product of two 275 individual qubits. The entanglement has been consumed and the 276 entangled state must be prepared again. 278 3. Entanglement as the fundamental resource 280 Entanglement is the fundamental building block of quantum networks. 281 Consider the state from the previous section: 283 (|00> + |11>)/sqrt(2). 285 Neither of the two qubits is in a definite |0> or |1> state and we 286 need to know the state of the entire register to be able to fully 287 describe the behaviour of the two qubits. 289 Entangled qubits have interesting non-local properties. Consider 290 sending one of the qubits to another device. This device could in 291 principle be anywhere: on the other side of the room, in a different 292 country, or even on a different planet. Provided negligible noise 293 has been introduced, the two qubits will forever remain in the 294 entangled state until a measurement is performed. The physical 295 distance does not matter at all for entanglement. 297 This lies at the heart of quantum networking, because it is possible 298 to leverage the non-classical correlations provided by entanglement 299 in order to design completely new types of application protocols that 300 are not possible to achieve with just classical communication. 301 Examples of such applications are quantum cryptography [Bennett14] 302 [Ekert91], blind quantum computation [Fitzsimons17], or distributed 303 quantum computation [Crepeau02]. 305 Entanglement has two very special features from which one can derive 306 some intuition about the types of applications enabled by a quantum 307 network. 309 The first stems from the fact that entanglement enables stronger than 310 classical correlations, leading to opportunities for tasks that 311 require coordination. As a trivial example, consider the problem of 312 consensus between two nodes who want to agree on the value of a 313 single bit. They can use the quantum network to prepare the state 314 (|00> + |11>)/sqrt(2) with each node holding one of the two qubits. 315 Once either of the two nodes performs a measurement, the state of the 316 two qubits collapses to either |00> or |11>, so whilst the outcome is 317 random and does not exist before measurement, the two nodes will 318 always measure the same value. We can also build the more general 319 multi-qubit state (|00...> + |11...>)/sqrt(2) and perform the same 320 algorithm between an arbitrary number of nodes. These stronger than 321 classical correlations generalise to more complicated measurement 322 schemes as well. 324 The second feature of entanglement is that it cannot be shared, in 325 the sense that if two qubits are maximally entangled with each other, 326 then it is physically impossible for any other system to have any 327 share of this entanglement [Terhal04]. Hence, entanglement forms a 328 sort of private and inherently untappable connection between two 329 nodes once established. 331 Entanglement is created through local interactions between two qubits 332 or as a product of the way the qubits were created (e.g. entangled 333 photon pairs). To create a distributed entangled state, one can then 334 physically send one of the qubits to a remote node. It is also 335 possible to directly entangle qubits that are physically separated, 336 but this still requires local interactions between some other qubits 337 that the separated qubits are initially entangled with. Therefore, 338 it is the transmission of qubits that draws the line between a 339 genuine quantum network and a collection of quantum computers 340 connected over a classical network. 342 A quantum network is defined as a collection of nodes that is able to 343 exchange qubits and distribute entangled states amongst themselves. 344 A quantum node that is able only to communicate classically with 345 another quantum node is not a member of a quantum network. 347 More complex services and applications can be built on top of 348 entangled states distributed by the network, see e.g. [ZOO] 350 4. Achieving quantum connectivity 352 This section explains the meaning of quantum connectivity and the 353 necessary physical processes at an abstract level. 355 4.1. Challenges 357 A quantum network cannot be built by simply extrapolating all the 358 classical models to their quantum analogues. Sending qubits over a 359 wire like we send classical bits is simply not as easy to do. There 360 are several technological as well as fundamental challenges that make 361 classical approaches unsuitable in a quantum context. 363 4.1.1. The measurement problem 365 In classical computers and networks we can read out the bits stored 366 in memory at any time. This is helpful for a variety of purposes 367 such as copying, error detection and correction, and so on. This is 368 not possible with qubits. 370 A measurement of a qubit's state will destroy its superposition and 371 with it any entanglement it may have been part of. Once a qubit is 372 being processed, it cannot be read out until a suitable point in the 373 computation, determined by the protocol handling the qubit, has been 374 reached. Therefore, we cannot use the same methods known from 375 classical computing for the purposes of error detection and 376 correction. Nevertheless, quantum error detection and correction 377 schemes exist that take this problem into account and how a network 378 chooses to manage errors will have an impact on its architecture. 380 4.1.2. No-cloning theorem 382 Since directly reading the state of a qubit is not possible, one 383 could ask if we can simply copy a qubit without looking at it. 385 Unfortunately, this is fundamentally not possible in quantum 386 mechanics [Park70] [Wootters82]. 388 The no-cloning theorem states that it is impossible to create an 389 identical copy of an arbitrary, unknown quantum state. Therefore, it 390 is also impossible to use the same mechanisms that worked for 391 classical networks for signal amplification, retransmission, and so 392 on as they all rely on the ability to copy the underlying data. 393 Since any physical channel will always be lossy, connecting nodes 394 within a quantum network is a challenging endeavour and its 395 architecture must at its core address this very issue. 397 4.1.3. Fidelity 399 In general, it is expected that a classical packet arrives at its 400 destination without any errors introduced by hardware noise along the 401 way. This is verified at various levels through a variety of error 402 detection and correction mechanisms. Since we cannot read or copy a 403 quantum state error detection and correction is more involved. 405 To describe the quality of a quantum state, a physical quantity 406 called fidelity is used [NielsenChuang]. Fidelity takes a value 407 between 0 and 1 -- higher is better, and less than 0.5 means the 408 state is unusable. It measures how close a quantum state is to the 409 state we have tried to create. It expresses the probability that one 410 state will pass a test to identify as the other. Fidelity is an 411 important property of a quantum system that allows us to quantify how 412 much a particular state has been affected by noise from various 413 sources (gate errors, channel losses, environment noise). 415 Interestingly, quantum applications do not need perfect fidelity to 416 be able to execute -- as long as the fidelity is above some 417 application-specific threshold, they will simply operate at lower 418 rates. Therefore, rather than trying to ensure that we always 419 deliver perfect states (a technologically challenging task) 420 applications will specify a minimum threshold for the fidelity and 421 the network will try its best to deliver it. A higher fidelity can 422 be achieved by either having hardware produce states of better 423 fidelity (sometimes one can sacrifice rate for higher fidelity) or by 424 employing quantum error detection and correction mechanisms. 426 4.1.4. Inadequacy of direct transmission 428 Conceptually, the most straightforward way to distribute an entangled 429 state is to simply transmit one of the qubits directly to the other 430 end across a series of nodes while performing sufficient forward 431 quantum error correction (Section 4.4.3.2) to bring losses down to an 432 acceptable level. Despite the no-cloning theorem and the inability 433 to directly measure a quantum state, error-correcting mechanisms for 434 quantum communication exist [Jiang09] [Fowler10] [Devitt13] 435 [Mural16]. However, quantum error correction makes very high demands 436 on both resources (physical qubits needed) and their initial 437 fidelity. Implementation is very challenging and quantum error 438 correction is not expected to be used until later generations of 439 quantum networks. 441 An alternative relies on the observation that we do not need to be 442 able to distribute any arbitrary entangled quantum state. We only 443 need to be able to distribute any one of what are known as the Bell 444 pair states [Briegel98]. 446 4.2. Bell pairs 448 Bell pair states are the entangled two-qubit states: 450 |00> + |11>, |00> - |11>, |01> + |10>, |01> - |10>, 452 where the constant 1/sqrt(2) normalisation factor has been ignored 453 for clarity. Any of the four Bell pair states above will do, as it 454 is possible to transform any Bell pair into another Bell pair with 455 local operations performed on only one of the qubits. When each 456 qubit in a Bell pair is held by a separate node, either node can 457 apply a series of single qubit gates to their qubit alone in order to 458 transform the state between the different variants. 460 Distributing a Bell pair between two nodes is much easier than 461 transmitting an arbitrary quantum state over a network. Since the 462 state is known, handling errors becomes easier and small-scale error- 463 correction (such as entanglement distillation discussed in a later 464 section) combined with reattempts becomes a valid strategy. 466 The reason for using Bell pairs specifically as opposed to any other 467 two-qubit state is that they are the maximally entangled two-qubit 468 set of basis states. Maximal entanglement means that these states 469 have the strongest non-classical correlations of all possible two- 470 qubit states. Furthermore, since single-qubit local operations can 471 never increase entanglement, less entangled states would impose some 472 constraints on distributed quantum algorithms. This makes Bell pairs 473 particularly useful as a generic building block for distributed 474 quantum applications. 476 4.3. Teleportation 478 The observation that we only need to be able to distribute Bell pairs 479 relies on the fact that this enables the distribution of any other 480 arbitrary entangled state. This can be achieved via quantum state 481 teleportation [Bennett93]. Quantum state teleportation consumes an 482 unknown qubit state that we want to transmit and recreates it at the 483 desired destination. This does not violate the no-cloning theorem as 484 the original state is destroyed in the process. 486 To achieve this, an entangled pair needs to be distributed between 487 the source and destination before teleportation commences. The 488 source then entangles the transmission qubit with its end of the pair 489 and performs a read out of the two qubits (the sum of these 490 operations is called a Bell state measurement). This consumes the 491 Bell pair's entanglement, turning the source and destination qubits 492 into independent states. The measurements yields two classical bits 493 which the source sends to the destination over a classical channel. 494 Based on the value of the received two classical bits, the 495 destination performs one of four possible corrections (called the 496 Pauli corrections) on its end of the pair, which turns it into the 497 unknown qubit state that we wanted to transmit. This requirement to 498 communicate the measurement read out over a classical channel 499 unfortunately means that entanglement cannot be used to transmit 500 information faster than the speed of light. 502 The unknown quantum state that was transmitted was never fed into the 503 network itself. Therefore, the network needs to only be able to 504 reliably produce Bell pairs between any two nodes in the network. 505 Thus, a key difference between a classical and quantum data planes is 506 that a classical one carries user data, but a quantum data plane 507 provides the resources for the user to transmit user data themselves 508 without further involvement of the network. 510 4.4. The life cycle of entanglement 512 Reducing the problem of quantum connectivity to one of generating a 513 Bell pair has facilitated the problem, but it has not solved it. In 514 this section, we discuss how these entangled pairs are generated in 515 the first place, and how their two qubits are delivered to the end- 516 points. 518 4.4.1. Elementary link generation 520 In a quantum network, entanglement is always first generated locally 521 (at a node or an auxiliary element) followed by a movement of one or 522 both of the entangled qubits across the link through quantum 523 channels. In this context, photons (particles of light) are the 524 natural candidate for entanglement carriers, called flying qubits. 525 The rationale for this choice is related to the advantages provided 526 by photons such as moderate interaction with the environment leading 527 to moderate decoherence, convenient control with standard optical 528 components, and high-speed, low-loss transmissions. However, since 529 photons are hard to store, a transducer must transfer the flying 530 qubit's state to a qubit suitable for information processing and/or 531 storage (often referred to as a matter qubit). 533 Since this process may fail, in order to generate and store 534 entanglement efficiently, we must be able to distinguish successful 535 attempts from failures. Entanglement generation schemes that are 536 able to announce successful generation are called heralded 537 entanglement generation schemes. 539 There exist three basic schemes for heralded entanglement generation 540 on a link through coordinated action of the two nodes at the two ends 541 of the link [Cacciapuoti19]: 543 o "At mid-point": in this scheme an entangled photon pair source 544 sitting midway between the two nodes with matter qubits sends an 545 entangled photon through a quantum channel to each of the nodes. 546 There, transducers are invoked to transfer the entanglement from 547 the flying qubits to the matter qubits. In this scheme, the 548 transducers know if the transfers succeeded and are able to herald 549 successful entanglement generation via a message exchange over the 550 classical channel. 552 o "At source": in this scheme one of the two nodes sends a flying 553 qubit that is entangled with one of its matter qubits. A 554 transducer at the other end of the link will transfer the 555 entanglement from the flying qubit to one of its matter qubits. 556 Just like in the previous scheme, the transducer knows if its 557 transfer succeeded and is able to herald successful entanglement 558 generation with a classical message sent to the other node. 560 o "At both end-points": in this scheme both nodes send a flying 561 qubit that is entangled with one of their matter qubits. A 562 detector somewhere in between the nodes performs a joint 563 measurement on the two qubits, which stochastically projects the 564 remote matter qubits into an entangled quantum state. The 565 detector knows if the entanglement succeeded and is able to herald 566 successful entanglement generation by sending a message to each 567 node over the classical channel. 569 The "mid-point source" scheme is more robust to photon loss, but in 570 the other schemes the nodes retain greater control over the entangled 571 pair generation. 573 Note that whilst photons travel in a particular direction through the 574 quantum channel the resulting entangled pair of qubits does not have 575 a direction associated with it. Physically, there is no upstream or 576 downstream end of the pair. 578 4.4.2. Entanglement swapping 580 The problem with generating entangled pairs directly across a link is 581 that efficiency decreases with channel length. Beyond a few 10s of 582 kilometres in optical fibre or 1000 kilometres in free space (via 583 satellite) the rate is effectively zero and due to the no-cloning 584 theorem we cannot simply amplify the signal. The solution is 585 entanglement swapping [Briegel98]. 587 A Bell pair between any two nodes in the network can be constructed 588 by combining the pairs generated along each individual link on a path 589 between the two end-points. Each node along the path can consume the 590 two pairs on the two links that it is connected to in order to 591 produce a new entangled pair between the two remote ends. This 592 process is known as entanglement swapping. Pictorially it can be 593 represented as follows: 595 +---------+ +---------+ +---------+ 596 | A | | B | | C | 597 | |------| |------| | 598 | X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 | 599 +---------+ +---------+ +---------+ 601 where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2 602 are the qubits of entangled pair Y. The entanglement is denoted with 603 ~~. In the diagram above, nodes A and B share the pair X and nodes B 604 and C share the pair Y, but we want entanglement between A and C. 606 To achieve this goal, we simply teleport the qubit X2 using the pair 607 Y. This requires node B to perform a Bell state measurement on the 608 qubits X2 and Y1 which result in the destruction of the entanglement 609 between Y1 and Y2. However, X2 is recreated in Y2's place, carrying 610 with it its entanglement with X1. The end-result is shown below: 612 +---------+ +---------+ +---------+ 613 | A | | B | | C | 614 | |------| |------| | 615 | X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 | 616 +---------+ +---------+ +---------+ 618 Depending on the needs of the network and/or application, a final 619 Pauli correction at the recipient node may not be necessary since the 620 result of this operation is also a Bell pair. However, the two 621 classical bits that form the read out from the measurement at node B 622 must still be communicated, because they carry information about 623 which of the four Bell pairs was actually produced. If a correction 624 is not performed, the recipient must be informed which Bell pair was 625 received. 627 This process of teleporting Bell pairs using other entangled pairs is 628 called entanglement swapping. Quantum nodes that create long- 629 distance entangled pairs via entanglement swapping are called quantum 630 repeaters in academic literature [Briegel98] and we will use the same 631 terminology in this memo. 633 4.4.3. Error Management 635 4.4.3.1. Distillation 637 Neither the generation of Bell pairs nor the swapping operations are 638 noiseless operations. Therefore, with each link and each swap the 639 fidelity of the state degrades. However, it is possible to create 640 higher fidelity Bell pair states from two or more lower fidelity 641 pairs through a process called distillation (sometimes also referred 642 to as purification) [Dur07]. 644 To distil a quantum state, a second (and sometimes third) quantum 645 state is used as a "test tool" to test a proposition about the first 646 state, e.g., "the parity of the two qubits in the first state is 647 even." When the test succeeds, confidence in the state is improved, 648 and thus the fidelity is improved. The test tool states are 649 destroyed in the process, so resource demands increase substantially 650 when distillation is used. When the test fails, the tested state 651 must also be discarded. Distillation makes low demands on fidelity 652 and resources compared to quantum error correction, but distributed 653 protocols incur round-trip delays due to classical communication 654 [Bennett96]. 656 4.4.3.2. Quantum Error Correction 658 Just like classical error correction, quantum error correction (QEC) 659 encodes logical qubits using several physical (raw) qubits to protect 660 them from errors described in Section 4.1.3 [Jiang09] [Fowler10] 661 [Devitt13] [Mural16]. Furthermore, similarly to its classical 662 counterpart, QEC can not only correct state errors but also account 663 for lost qubits. Additionally, if all physical qubits which encode a 664 logical qubit are located at the same node, the correction procedure 665 can be executed locally, even if the logical qubit is entangled with 666 remote qubits. 668 Although QEC was originally a scheme proposed to protect a qubit from 669 noise, QEC can also be applied to entanglement distillation. Such 670 QEC-applied distillation is cost-effective but requires a higher base 671 fidelity. 673 4.4.3.3. Error management schemes 675 Quantum networks have been categorized into three "generations" based 676 on the error management scheme they employ [Mural16]. Note that 677 these "generations" are more like categories; they do not necessarily 678 imply a time progression and do not obsolete each other, though the 679 later generations do require more advanced technologies. Which 680 generation is used depends on the hardware platform and network 681 design choices. 683 Table 1 summarises the generations. 685 +-----------+-----------------+------------------------+------------+ 686 | | First | Second generation | Third | 687 | | generation | | generation | 688 +-----------+-----------------+------------------------+------------+ 689 | Loss | Heralded | Heralded entanglement | Quantum | 690 | tolerance | entanglement | generation (bi- | Error | 691 | | generation (bi- | directional classical | Correction | 692 | | directional | signaling) | (no | 693 | | classical | | classical | 694 | | signaling) | | signaling) | 695 | | | | | 696 | Error | Entanglement | Entanglement | Quantum | 697 | tolerance | distillation | distillation (uni- | Error | 698 | | (bi-directional | directional classical | Correction | 699 | | classical | signaling) or | (no | 700 | | signaling) | Quantum Error | classical | 701 | | | Correction (no | signaling) | 702 | | | classical signaling) | | 703 +-----------+-----------------+------------------------+------------+ 705 Table 1: Classical signaling and generations 707 Generations are defined by the directions of classical signalling 708 required in their distributed protocols for loss tolerance and error 709 tolerance. Classical signalling carries the classical bits and 710 incurs round-trip delays described in Section 4.4.3.1, hence they 711 affect the performance of quantum networks, especially as the 712 distance between the communicating nodes increases. 714 Loss tolerance is about tolerating qubit transmission losses between 715 nodes. Heralded entanglement generation, as described in 716 Section 4.4.1, confirms the receipt of an entangled qubit using a 717 heralding signal. A pair of directly connected quantum nodes 718 repeatedly attempt to generate an entangled pair until the a 719 heralding signal is received. As described in Section 4.4.3.2, QEC 720 can be applied to complement lost qubits eliminating the need for re- 721 attempts. Furthermore, since the correction procedure is composed of 722 local operations, it does not require a heralding signal. However, 723 it is possible only when the photon loss rate from transmission to 724 measurement is less than 50%. 726 Error tolerance is about tolerating quantum state errors. 727 Entanglement distillation is the easiest mechanism for improved error 728 tolerance to implement, but it incurs round-trip delays due the 729 requirement for bi-directional classical signalling. The 730 alternative, QEC, is able to correct state errors locally so that it 731 does not need any classical signalling between the quantum nodes. In 732 between these two extremes, there is also QEC-applied distillation, 733 which requires uni-directional classical signalling. 735 The three "generations" summarised: 737 1. First generation quantum networks use heralding for loss 738 tolerance and entanglement distillation for error tolerance. 739 These networks can be implemented even with a limited set of 740 available quantum gates. 742 2. Second generation quantum networks improve upon the first 743 generation with QEC codes for error tolerance (but not loss 744 tolerance). At first, QEC will be applied to entanglement 745 distillation only which requires uni-directional classical 746 signalling. Later, QEC codes will be used to create logical Bell 747 pairs which no longer require any classical signalling for the 748 purposes of error tolerance. Heralding is still used to 749 compensate for transmission losses. 751 3. Third generation quantum networks directly transmit QEC encoded 752 qubits to adjacent nodes, as discussed in Section 4.1.4. 753 Elementary link Bell pairs can now be created without heralding 754 or any other classical signalling. Furthermore, this also 755 enables direct transmission architectures in which qubits are 756 forwarded end-to-end like classical packets rather than relying 757 on Bell pairs and entanglement swapping. 759 4.4.4. Delivery 761 Eventually, the Bell pairs must be delivered to an application (or 762 higher layer protocol) at the two end-nodes. A detailed list of such 763 requirements is beyond the scope of this memo. At minimum, the end- 764 nodes require information to map a particular Bell pair to the qubit 765 in their local memory that is part of this entangled pair. 767 5. Architecture of a quantum internet 769 It is evident from the previous sections that the fundamental service 770 provided by a quantum network significantly differs from that of a 771 classical network. Therefore, it is not surprising that the 772 architecture of a quantum internet will itself be very different from 773 that of the classical Internet. 775 5.1. Challenges 777 This subsection covers the major fundamental challenges building 778 quantum networks. Here, we only describe the fundamental 779 differences. Technological limitations are described later. 781 1. Bell pairs are not equivalent to payload carrying packets. 783 In most classical networks, including Ethernet, Internet Protocol 784 (IP), and Multi-Protocol Label Switching (MPLS) networks, user 785 data is grouped into packets. In addition to the user data, each 786 packet also contains a series of headers which contain the 787 control information that lets routers and switches forward it 788 towards its destination. Packets are the fundamental unit in a 789 classical network. 791 In a quantum network, the entangled pairs of qubits are the basic 792 unit of networking. These qubits themselves do not carry any 793 headers. Therefore, quantum networks will have to send all 794 control information via separate classical channels which the 795 repeaters will have to correlate with the qubits stored in their 796 memory. 798 2. "Store and forward" vs "store and swap" quantum networks. 800 As described in Section 4.4.1, quantum links provide Bell pairs 801 that are undirected network resources, in contrast to directed 802 frames of classical networks. This phenomenological distinction 803 leads to architectural differences between quantum networks and 804 classical networks. Quantum networks combine multiple elementary 805 link Bell pairs together to create one an end-to-end Bell pair, 806 whereas classical networks deliver messages from one end to the 807 other end hop by hop. 809 Classical networks receive data on one interface, store it in 810 local buffers, then forward the data to another appropriate 811 interface. Quantum networks store Bell pairs and then execute 812 entanglement swapping instead of forwarding in the data plane. 813 Such quantum networks are "store and swap" networks. In "store 814 and swap" networks, we do not need to care about the order in 815 which the Bell pairs were generated since they are undirected. 816 This distinction makes control algorithms and optimisation of 817 quantum networks different from classical ones. Note that third 818 generation quantum networks, as described in Section 4.4.1, will 819 be able to support a "store and forward" architecture in addition 820 to "store and swap". 822 3. An entangled pair is only useful if the locations of both qubits 823 are known. 825 A classical network packet logically exists only at one location 826 at any point in time. If a packet is modified in some way, 827 whether headers or payload, this information does not need to be 828 conveyed to anybody else in the network. The packet can be 829 simply forwarded as before. 831 In contrast, entanglement is a phenomenon in which two or more 832 qubits exist in a physically distributed state. Operations on 833 one of the qubits change the mutual state of the pair. Since the 834 owner of a particular qubit cannot just read out its state, it 835 must coordinate all its actions with the owner of the pair's 836 other qubit. Therefore, the owner of any qubit that is part of 837 an entangled pair must know the location of its counterpart. 838 Location, in this context, need not be the explicit spatial 839 location. A relevant pair identifier, a means of communication 840 between the pair owners, and an association between the pair ID 841 and the individual qubits is sufficient. 843 4. Generating entanglement requires temporary state. 845 Packet forwarding in a classical network is largely a stateless 846 operation. When a packet is received, the router does a lookup 847 in its forwarding table and sends the packet out of the 848 appropriate output. There is no need to keep any memory of the 849 packet any more. 851 A quantum node must be able to make decisions about qubits that 852 it receives and is holding in its memory. Since qubits do not 853 carry headers, the receipt of an entangled pair conveys no 854 control information based on which the repeater can make a 855 decision. The relevant control information will arrive 856 separately over a classical channel. This implies that a 857 repeater must store temporary state as the control information 858 and the qubit it pertains to will, in general, not arrive at the 859 same time. 861 5.2. Classical communication 863 In this memo we have already covered two different roles that 864 classical communication must perform: 866 o communicate classical bits of information as part of distributed 867 protocols such as entanglement swapping and teleportation, 869 o communicate control information within a network, including both 870 background protocols such as routing as well as signalling 871 protocols to set up end-to-end entanglement generation. 873 Classical communication is a crucial building block of any quantum 874 network. All nodes in a quantum network are assumed to have 875 classical connectivity with each other (within typical administrative 876 domain limts). Therefore, quantum nodes will need to manage two data 877 planes in parallel, a classical one and a quantum one. Additionally, 878 a node must be able to correlate information between the two planes 879 so that the control information received on a classical channel can 880 be applied to the qubits managed by the quantum data plane. 882 5.3. Abstract model of the network 884 5.3.1. The control and data planes 886 Control plane protocols for quantum networks will have many 887 responsibilities similar to their classical counterparts, namely 888 drawing the network topology, resource management, populating data 889 plane tables, etc. Most of these protocols do not require the 890 manipulation of quantum data and can operate simply by exchanging 891 classical messages only. There may also be some control plane 892 functionality that does require the handling of quantum data, e.g. a 893 quantum ping [I-D.irtf-qirg-quantum-internet-use-cases]. As it is 894 not clear if there is much benefit in defining a separate quantum 895 control plane given the significant overlap in responsibilities with 896 its classical counterpart, the question of whether there should be a 897 separate quantum control plane is beyond the scope of this document. 899 However, the data plane separation is much more distinct and there 900 will be two data planes: a classical data plane and a quantum data 901 plane. The classical data plane processes and forwards classical 902 packets. The quantum data plane processes and swaps entangled pairs. 903 Third generation quantum networks may also forward qubits in addition 904 to swapping Bell pairs. 906 In addition to control plane messages, there will also be control 907 information messages that operate at the granularity of individual 908 entangled pairs, such as heralding messages used for elementary link 909 generation (Section 4.4.1). In terms of functionality, these 910 messages are closer to classical packet headers than control plane 911 messages and thus we consider them to be part of the quantum data 912 plane. Therefore, a quantum data plane also includes the exchange of 913 classical control information at the granularity of individual qubits 914 and entangled pairs. 916 5.3.2. Elements of a quantum network 918 We have identified quantum repeaters as the core building block of a 919 quantum network. However, a quantum repeater will have to do more 920 than just entanglement swapping in a functional quantum network. Its 921 key responsibilities will include: 923 1. Creating link-local entanglement between neighbouring nodes. 925 2. Extending entanglement from link-local pairs to long-range pairs 926 through entanglement swapping. 928 3. Performing distillation to manage the fidelity of the produced 929 pairs. 931 4. Participating in the management of the network (routing, etc.). 933 Not all quantum repeaters in the network will be the same; here we 934 break them down further: 936 o Quantum routers (controllable quantum nodes) - A quantum router is 937 a quantum repeater with a control plane that participates in the 938 management of the network and will make decisions about which 939 qubits to swap to generate the requested end-to-end pairs. 941 o Automated quantum nodes - An automated quantum node is a data 942 plane only quantum repeater that does not participate in the 943 network control plane. Since the no-cloning theorem precludes the 944 use of amplification, long-range links will be established by 945 chaining multiple such automated nodes together. 947 o End-nodes - End-nodes in a quantum network must be able to receive 948 and handle an entangled pair, but they do not need to be able to 949 perform an entanglement swap (and thus are not necessarily quantum 950 repeaters). End-nodes are also not required to have any quantum 951 memory as certain quantum applications can be realised by having 952 the end-node measure its qubit as soon as it is received. 954 o Non-quantum nodes - Not all nodes in a quantum network need to 955 have a quantum data plane. A non-quantum node is any device that 956 can handle classical network traffic. 958 Additionally, we need to identify two kinds of links that will be 959 used in a quantum network: 961 o Quantum links - A quantum link is a link which can be used to 962 generate an entangled pair between two directly connected quantum 963 repeaters. This may include additional mid-point elements 964 described in Section 4.4.1. It may also include a dedicated 965 classical channel that is to be used solely for the purpose of 966 coordinating the entanglement generation on this quantum link. 968 o Classical links - A classical link is a link between any node in 969 the network that is capable of carrying classical network traffic. 971 Note that passive elements, such as optical switches, do not destroy 972 the quantum state. Therefore, it is possible to connect multiple 973 quantum nodes with each other over an optical network and perform 974 optical switching rather than routing via entanglement swapping at 975 quantum routers. This does require coordination with the elementary 976 link entanglement generation process and it still requires repeaters 977 to overcome the short-distance limitations. However, this is a 978 potentially feasible architecture for local area networks. 980 5.3.3. Putting it all together 982 A two-hop path in a generic quantum network can be represented as: 984 | App |-------------------CC-------------------| App | 985 || || 986 ------ ------ ------ 987 | EN |----QL & CC----| QR |----QL & CC----| EN | 988 ------ ------ ------ 990 App - user-level application 991 QR - quantum repeater 992 EN - end-node 993 QL - quantum link 994 CC - classical channel (can consist of many classical links) 996 An application running on two end-nodes attached to a network will at 997 some point need the network to generate entangled pairs for its use. 998 This may require negotiation between the end-nodes (possibly ahead of 999 time), because they must both open a communication end-point which 1000 the network can use to identify the two ends of the connection. The 1001 two end-nodes use the classical connectivity available in the network 1002 to achieve this goal. 1004 When the network receives a request to generate end-to-end entangled 1005 pairs it uses the classical communication channels to coordinate and 1006 claim the resources necessary to fulfill this request. This may be 1007 some combination of prior control information (e.g. routing tables) 1008 and signalling protocols, but the details of how this is achieved are 1009 an active research question and thus beyond the scope of this memo. 1011 During or after the distribution of control information, the network 1012 performs the necessary quantum operations such as generating 1013 entanglement over individual links, performing entanglement swaps, 1014 and further signalling to transmit the swap outcomes and other 1015 control information. Since Bell pairs do not carry any user data, 1016 some of these operations can be performed before the request is 1017 received in anticipation of the demand. 1019 The entangled pair is delivered to the application once it is ready, 1020 together with the relevant pair identifier. However, being ready 1021 does not necessarily mean that all link pairs and entanglement swaps 1022 are complete, as some applications can start executing on an 1023 incomplete pair. In this case the remaining entanglement swaps will 1024 propagate the actions across the network to the other end, sometimes 1025 necessitating fixup operations at the end node. 1027 5.4. Network boundaries 1029 Just like classical networks, various boundaries will exist in 1030 quantum networks. 1032 5.4.1. Boundaries between different physical architectures 1034 There are many different physical architectures for implementing 1035 quantum repeater technology. The different technologies differ in 1036 how they store and manipulate qubits in memory and how they generate 1037 entanglement across a link with their neighbours. Different 1038 architectures come with different trade-offs and thus a functional 1039 network will likely consist of a mixture of different types of 1040 quantum repeaters. 1042 For example, architectures based on optical elements and atomic 1043 ensembles [Sangouard11] are very efficient at generating 1044 entanglement, but provide little control over the qubits once the 1045 pair is generated. On the other hand, nitrogen-vacancy architectures 1046 [Hensen15] offer a much greater degree of control over qubits, but 1047 have a harder time generating the entanglement across a link. 1049 It is an open research question where exactly the boundary will lie. 1050 It could be that a single quantum repeater node provides some 1051 backplane connection between the architectures, but it also could be 1052 that special quantum links delineate the boundary. 1054 5.4.2. Boundaries between different administrative regions 1056 Just like in classical networks, multiple quantum networks will 1057 connect into a global quantum internet. This necessarily implies the 1058 existence of borders between different administrative regions. How 1059 these boundaries will be handled is also an open question and thus 1060 beyond the scope of this memo. 1062 5.4.3. Boundaries between different error management schemes 1064 Not only are there physical differences and administrative 1065 boundaries, but there are important distinctions in how errors will 1066 be managed, as described in Section 4.4.3.3, which affect the content 1067 and semantics of messages that must cross those boundaries -- both 1068 for connection setup and real-time operation [Nagayama16]. How to 1069 interconnect those schemes is also an open research question. 1071 5.5. Physical constraints 1073 The model above has effectively abstracted away the particulars of 1074 the hardware implementation. However, certain physical constraints 1075 need to be considered in order to build a practical network. Some of 1076 these are fundamental constraints and no matter how much the 1077 technology improves, they will always need to be addressed. Others 1078 are artefacts of the early stages of a new technology. Here, we 1079 consider a highly abstract scenario and refer to [Wehner18] for 1080 pointers to the physics literature. 1082 5.5.1. Memory lifetimes 1084 In addition to discrete operations being imperfect, storing a qubit 1085 in memory is also highly non-trivial. The main difficulty in 1086 achieving persistent storage is that it is extremely challenging to 1087 isolate a quantum system from the environment. The environment 1088 introduces an uncontrollable source of noise into the system which 1089 affects the fidelity of the state. This process is known as 1090 decoherence. Eventually, the state has to be discarded once its 1091 fidelity degrades too much. 1093 The memory lifetime depends on the particular physical setup, but the 1094 highest achievable values in quantum network hardware currently are 1095 on the order of seconds [Abobeih18] although a lifetime of a minute 1096 has also been demonstrated for qubits not connected to a quantum 1097 network [Bradley19] (as of 2020). These values have increased 1098 tremendously over the lifetime of the different technologies and are 1099 bound to keep increasing. However, if quantum networks are to be 1100 realised in the near future, they need to be able to handle short 1101 memory lifetimes, for example by reducing latency on critical paths. 1103 5.5.2. Rates 1105 Entanglement generation on a link between two connected nodes is not 1106 a very efficient process and it requires many attempts to succeed 1107 [Hensen15] [Dahlberg19]. Currently, the highest achievable rates of 1108 success between nodes capable of storing the resulting qubits are on 1109 the order of 10 Hz. Combined with short memory lifetimes this leads 1110 to very tight timing windows to build up network-wide connectivity. 1112 5.5.3. Communication qubits 1114 Most physical architectures capable of storing qubits are only able 1115 to generate entanglement using only a subset of available qubits 1116 called communication qubits [Dahlberg19]. Once a Bell pair has been 1117 generated using a communication qubit, its state can be transferred 1118 into memory. This may impose additional limitations on the network. 1119 In particular, if a given node has only one communication qubit it 1120 cannot simultaneously generate Bell pairs over two links. It must 1121 generate entanglement over the links one at a time. 1123 5.5.4. Homogeneity 1125 Currently all hardware implementations are homogeneous and they do 1126 not interface with each other. In general, it is very challenging to 1127 combine different quantum information processing technologies at 1128 present. Coupling different technologies with each other is of great 1129 interest as it may help overcome the weaknesses of the different 1130 implementations, but this may take a long time to be realised with 1131 high reliability and thus is not a near-term goal. 1133 6. Architectural principles 1135 Given that the most practical way of realising quantum network 1136 connectivity is using Bell pair and entanglement swapping repeater 1137 technology, what sort of principles should guide us in assembling 1138 such networks such that they are functional, robust, efficient, and 1139 most importantly, they work? Furthermore, how do we design networks 1140 so that they work under the constraints imposed by the hardware 1141 available today, but do not impose unnecessary burdens on future 1142 technology? 1144 As quantum networking is a completely new technology that is likely 1145 to see many iterations over its lifetime, this memo must not serve as 1146 a definitive set of rules, but merely as a general set of recommended 1147 guidelines for the first generations of quantum networks based on 1148 principles and observations made by the community. The benefit of 1149 having a community built document at this early stage is that 1150 expertise in both quantum information and network architecture is 1151 needed in order to successfully build a quantum internet. 1153 6.1. Goals of a quantum internet 1155 When outlining any set of principles we must ask ourselves what goals 1156 do we want to achieve as inevitably trade-offs must be made. So what 1157 sort of goals should drive a quantum network architecture? The 1158 following list has been inspired by the history of computer 1159 networking and thus it is inevitably very similar to one that could 1160 be produced for the classical Internet [Clark88]. However, whilst 1161 the goals may be similar the challenges involved are often 1162 fundamentally different. The list will also most likely evolve with 1163 time and the needs of its users. 1165 1. Support distributed quantum applications 1167 This goal seems trivially obvious, but makes a subtle, but 1168 important point which highlights a key difference between quantum 1169 and classical networks. Ultimately, quantum data transmission is 1170 not the goal of a quantum network - it is only one possible 1171 component of more advanced quantum application protocols 1172 [Wehner18]. Whilst transmission certainly could be used as a 1173 building block for all quantum applications, it is not the most 1174 basic one possible. For example, entanglement-based QKD, the 1175 most well known quantum application protocol, only relies on the 1176 stronger-than-classical correlations and inherent secrecy of 1177 entangled Bell pairs and does not have to transmit arbitrary 1178 quantum states [Ekert91]. 1180 The primary purpose of a quantum internet is to support 1181 distributed quantum application protocols and it is of utmost 1182 importance that they can run well and efficiently. Thus, it is 1183 important to develop performance metrics meaningful to 1184 application to drive the development of quantum network 1185 protocols. For example, the Bell pair generation rate is 1186 meaningless if one does not also consider their fidelity. It is 1187 generally much easier to generate pairs of lower fidelity, but 1188 quantum applications may have to make multiple re-attempts or 1189 even abort if the fidelity is too low. A review of the 1190 requirements for different known quantum applications can be 1191 found in [Wehner18] and an overview of use-cases can be found in 1192 [I-D.irtf-qirg-quantum-internet-use-cases]. 1194 2. Support tomorrow's distributed quantum applications 1196 The only principle of the Internet that should survive 1197 indefinitely is the principle of constant change [RFC1958]. 1199 Technical change is continuous and the size and capabilities of 1200 the quantum internet will change by orders of magnitude. 1201 Therefore, it is an explicit goal that a quantum internet 1202 architecture be able to embrace this change. We have the benefit 1203 of having been witness to the evolution of the classical Internet 1204 over several decades and seen what worked and what did not. It 1205 is vital for a quantum internet to avoid the need for flag days 1206 (e.g. NCP to TCP/IP) or upgrades that take decades to roll out 1207 (e.g. IPv4 to IPv6). 1209 Therefore, it is important that any proposed architecture for 1210 general purpose quantum repeater networks can integrate new 1211 devices and solutions as they become available. The architecture 1212 should not be constrained due to considerations for early-stage 1213 hardware and applications. For example, it is already possible 1214 to run QKD efficiently on metropolitan scales and such networks 1215 are already commercially available. However, they are not based 1216 on quantum repeaters and thus will not be able to easily 1217 transition to more sophisticated applications. 1219 3. Support heterogeneity 1221 There are multiple proposals for realising practical quantum 1222 repeater hardware and they all have their advantages and 1223 disadvantages. Some may offer higher Bell pair generation rates 1224 on individual links at the cost of more difficult entanglement 1225 swap operations. Other platforms may be good all around, but are 1226 more difficult to build. 1228 In addition to physical boundaries, there may be distinctions in 1229 how errors are managed (Section 4.4.3.3). These difference will 1230 affect the content and semantics of messages that cross these 1231 boundaries -- both for connection setup and real-time operation. 1233 The optimal network configuration will likely leverage the 1234 advantages of multiple platforms to optimise the provided 1235 service. Therefore, it is an explicit goal to incorporate varied 1236 hardware and technology support from the beginning. 1238 4. Ensure security at the network level 1240 The question of security in quantum networks is just as critical 1241 as it is in the classical Internet, especially since enhanced 1242 security offered by quantum entanglement is one of the key 1243 driving factors. 1245 It turns out that as long as the underlying implementation 1246 corresponds to (or sufficiently approximates) theoretical models 1247 of quantum cryptography, quantum cryptographic protocols do not 1248 need the network to provide any guarantees about the 1249 confidentiality or integrity of the transmitted qubits or the 1250 generated entanglement. Instead, applications, such as QKD, 1251 establish such guarantees in an end-to-end fashion using the 1252 classical network in conjunction with the quantum one. 1254 Nevertheless, whilst applications can ensure their own secure 1255 operation, network protocols themselves should be security aware 1256 in order to protect the network itself and limit disruption. 1257 Whilst the applications remain secure they are not necessarily 1258 operational or as efficient in the presence of an attacker. 1259 Security concerns in quantum networks are described in more 1260 detail in [Satoh17] [Satoh20]. 1262 5. Make them easy to monitor 1264 In order to manage, evaluate the performance of, or debug a 1265 network it is necessary to have the ability to monitor the 1266 network while ensuring there will be mechanisms in place to 1267 protect the confidentiality and integrity of the devices 1268 connected to it. Quantum networks bring new challenges in this 1269 area so it should be a goal of a quantum network architecture to 1270 make this task easy. 1272 The fundamental unit of quantum information, the qubit, cannot be 1273 actively monitored as any readout irreversibly destroys its 1274 contents. One of the implications of this fact is that measuring 1275 an individual pair's fidelity is impossible. Fidelity is 1276 meaningful only as a statistical quantity which requires the 1277 constant monitoring and the sacrifice of generated Bell pairs for 1278 tomography or other methods. 1280 Furthermore, given one end of an entangled pair, it is impossible 1281 to tell where the other qubit is without any additional classical 1282 metadata. It is impossible to extract this information from the 1283 qubits themselves. This implies that tracking entangled pairs 1284 necessitates some exchange of classical information. This 1285 information might include (i) a reference to the entangled pair 1286 that allows distributed applications to coordinate actions on 1287 qubits of the same pair, (ii) the two bits from each entanglement 1288 swap necessary to identify the final state of the Bell pair 1289 (Section 4.4.2). 1291 6. Ensure availability and resilience 1293 Any practical and usable network, classical or quantum, must be 1294 able to continue to operate despite losses and failures, and be 1295 robust to malicious actors trying to disable connectivity. What 1296 differs in quantum networks as compared to classical networks in 1297 this regard is that we now have two data planes and two types of 1298 channels to worry about: a quantum and a classical one. 1299 Therefore, availability and resilience will most likely require a 1300 more advanced treatment than they do in classical networks. 1302 6.2. The principles of a quantum internet 1304 The principles support the goals, but are not goals themselves. The 1305 goals define what we want to build and the principles provide a 1306 guideline in how we might achieve this. The goals will also be the 1307 foundation for defining any metric of success for a network 1308 architecture, whereas the principles in themselves do not distinguish 1309 between success and failure. For more information about design 1310 considerations for quantum networks see [VanMeter13.1] [Dahlberg19]. 1312 1. Entanglement is the fundamental service 1314 The key service that a quantum network provides is the 1315 distribution of entanglement between the nodes in a network. All 1316 distributed quantum applications are built on top of this key 1317 resource. Bell pairs are the minimal entanglement building block 1318 that is sufficient to develop these applications. However, a 1319 quantum network may also distribute multipartite entangled states 1320 (entangled states of three or more qubits) [Meignant19] as this 1321 may be more efficient under certain circumstances. 1323 2. Bell Pairs are indistinguishable 1325 Any two Bell Pairs between the same two nodes are 1326 indistinguishable for the purposes of an application provided 1327 they both satisfy its required fidelity threshold. This 1328 observation is likely to be key in enabling a more optimal 1329 allocation of resources in a network, e.g. for the purposes of 1330 provisioning resources to meet application demand. However, the 1331 qubits that make up the pair themselves are not indistinguishable 1332 and the two nodes operating on a pair must coordinate to make 1333 sure they are operating on qubits that belong to the same Bell 1334 pair. 1336 3. Fidelity is part of the service 1338 In addition to being able to deliver Bell pairs to the 1339 communication end-points, the Bell Pairs must be of sufficient 1340 fidelity. Unlike in classical networks where errors are 1341 effectively eliminated before reaching the application, many 1342 quantum applications only need imperfect entanglement to 1343 function. However, quantum applications will generally have a 1344 threshold for Bell pair fidelity below which they are no longer 1345 able to operate. Different applications will have different 1346 requirements for what fidelity they can work with. It is the 1347 network's responsibility to balance the resource usage with 1348 respect to the applications' requirements. It may be that it is 1349 cheaper for the network to provide lower fidelity pairs that are 1350 just above the threshold required by the application than it is 1351 to guarantee high fidelity pairs to all applications regardless 1352 of their requirements. 1354 4. Time is an expensive resource 1356 Time is not the only resource that is in short supply (memory, 1357 and communication qubits are as well), but ultimately it is the 1358 lifetime of quantum memories that imposes some of the most 1359 difficult conditions for operating an extended network of quantum 1360 nodes. Current hardware has low rates of Bell pair generation, 1361 short memory lifetimes, and access to a limited number of 1362 communication qubits. All these factors combined mean that even 1363 a short waiting queue at some node could be enough for a Bell 1364 pair to decohere or result in an end-to-end pair below an 1365 application's fidelity threshold. Therefore, managing the idle 1366 time of qubits holding live quantum states should be done 1367 carefully. Ideally by minimising the idle time, but potentially 1368 also by moving the quantum state for temporary storage to a 1369 quantum memory with a longer lifetime. 1371 5. Be flexible with regards to capabilities and limitations 1373 This goal encompasses two important points. First, the 1374 architecture should be able to function under the physical 1375 constraints imposed by the current generation hardware. Near- 1376 future hardware will have low entanglement generation rates, 1377 quantum memories able to hold a handful of qubits at best, and 1378 decoherence rates that will render many generated pairs unusable. 1380 Second, the architecture should not make it difficult to run the 1381 network over any hardware that may come along in the future. The 1382 physical capabilities of repeaters will improve and redeploying a 1383 technology is extremely challenging. 1385 7. A thought experiment inspired by classical networks 1387 To conclude, we discuss a plausible quantum network architecture 1388 inspired by MPLS. This is not an architecture proposal, but rather a 1389 thought experiment to give the reader an idea of what components are 1390 necessary for a functional quantum network. We use classical MPLS as 1391 a basis as it is well known and understood in the networking 1392 community. 1394 Creating end-to-end Bell pairs between remote end-points is a 1395 stateful distributed task that requires a lot of a-priori 1396 coordination. Therefore, a connection-oriented approach seems the 1397 most natural for quantum networks. In connection-oriented quantum 1398 networks, when two quantum application end-points wish to start 1399 creating end-to-end Bell pairs, they must first create a quantum 1400 virtual circuit (QVC). As an analogy, in MPLS networks end-points 1401 must establish a label switched path (LSP) before exchanging traffic. 1402 Connection-oriented quantum networks may also support virtual 1403 circuits with multiple end-points for creating multipartite 1404 entanglement. As an analogy, MPLS networks have the concept of 1405 multi-point LSPs for multicast. 1407 When a quantum application creates a quantum virtual circuit, it can 1408 indicate quality of service (QoS) parameters such as the required 1409 capacity in end-to-end Bell pairs per second (BPPS) and the required 1410 fidelity of the Bell pairs. As an analogy, in MPLS networks 1411 applications specify the required bandwidth in bits per second (BPS) 1412 and other constraints when they create a new LSP. 1414 Quantum networks need a routing function to compute the optimal path 1415 (i.e. the best sequence of routers and links) for each new quantum 1416 virtual circuit. The routing function may be centralized or 1417 distributed. In the latter case, the quantum network needs a 1418 distributed routing protocol. As an analogy, classical networks use 1419 routing protocols such as open shortest path first (OSPF) and 1420 intermediate-system to intermediate system (IS-IS). However, note 1421 that the definition of "shortest-path"/"least-cost" may be different 1422 in a quantum network to account for its non-classical features, such 1423 as fidelity [VanMeter13.2]. 1425 Given the very scarce availability of resources in early quantum 1426 networks, a traffic engineering function is likely to be beneficial. 1427 Without traffic engineering, quantum virtual circuits always use the 1428 shortest path. In this case, the quantum network cannot guarantee 1429 that each quantum end-point will get its Bell pairs at the required 1430 rate or fidelity. This is analogous to "best effort" service in 1431 classical networks. 1433 With traffic engineering, quantum virtual circuits choose a path that 1434 is guaranteed to have the requested resources (e.g. bandwidth in 1435 BPPS) available, taking into account the capacity of the routers and 1436 links and taking into account the resources already consumed by other 1437 virtual circuits. As an analogy, both OSPF and IS-IS have traffic 1438 engineering (TE) extensions to keep track of used and available 1439 resources, and can use constrained shortest path first (CSPF) to take 1440 resource availability and other constraints into account when 1441 computing the optimal path. 1443 The use of traffic engineering implies the use of call admission 1444 control (CAC): the network denies any virtual circuits for which it 1445 cannot guarantee the requested quality of service a-priori. Or 1446 alternatively, the network pre-empts lower priority circuits to make 1447 room for the new one. 1449 Quantum networks need a signaling function: once the path for a 1450 quantum virtual circuit has been computed, signaling is used to 1451 install the "forwarding rules" into the data plane of each quantum 1452 router on the path. The signaling may be distributed, analogous to 1453 the resource reservation protocol (RSVP) in MPLS. Or the signaling 1454 may be centralized, similar to OpenFlow. 1456 Quantum networks need an abstraction of the hardware for specifying 1457 the forwarding rules. This allows us to de-couple the control plane 1458 (routing and signaling) from the data plane (actual creation of Bell 1459 pairs). The forwarding rules are specified using abstract building 1460 blocks such as "creating local Bell pairs", "swapping Bell pairs", 1461 "distillation of Bell pairs". As an analogy, classical networks use 1462 abstractions that are based on match conditions (e.g. looking up 1463 header fields in tables) and actions (e.g. modifying fields or 1464 forwarding a packet to a specific interface). The data-plane 1465 abstractions in quantum networks will be very different from those in 1466 classical networks due to the fundamental differences in technology 1467 and the stateful nature of quantum networks. In fact, choosing the 1468 right abstractions will be one of the biggest challenges when 1469 designing interoperable quantum network protocols. 1471 In quantum networks, control plane traffic (routing and signaling 1472 messages) is exchanged over a classical channel, whereas data plane 1473 traffic (the actual Bell pair qubits) is exchanged over a separate 1474 quantum channel. This is in contrast to most classical networks, 1475 where control plane traffic and data plane traffic share the same 1476 channel and where a single packet contains both user fields and 1477 header fields. There is, however, a classical analogy to the way 1478 quantum networks work. Generalized MPLS (GMPLS) networks use 1479 separate channels for control plane traffic and data plane traffic. 1480 Furthermore, GMPLS networks support data planes where there is no 1481 such thing as data plane headers (e.g. DWDM or TDM networks). 1483 8. Security Considerations 1485 Security is listed as an explicit goal for the architecture and this 1486 issue is addressed in the section on goals. However, as this is an 1487 informational memo it does not propose any concrete mechanisms to 1488 achieve these goals. 1490 9. IANA Considerations 1492 This memo includes no request to IANA. 1494 10. Acknowledgements 1496 The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel 1497 Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang, 1498 Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG 1499 community as a whole for their very useful reviews and comments to 1500 the document. 1502 11. Informative References 1504 [Abobeih18] 1505 Abobeih, M., Cramer, J., Bakker, M., Kalb, N., Markham, 1506 M., Twitchen, D., and T. 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Zurek, "A single quantum cannot be 1763 cloned", Nature Vol. 299, Iss. 5886, pp. 802-803, 1982, 1764 . 1766 [ZOO] "The Quantum Protocol Zoo", . 1768 Authors' Addresses 1770 Wojciech Kozlowski 1771 QuTech 1772 Building 22 1773 Lorentzweg 1 1774 Delft 2628 CJ 1775 Netherlands 1777 Email: w.kozlowski@tudelft.nl 1779 Stephanie Wehner 1780 QuTech 1781 Building 22 1782 Lorentzweg 1 1783 Delft 2628 CJ 1784 Netherlands 1786 Email: s.d.c.wehner@tudelft.nl 1788 Rodney Van Meter 1789 Keio University 1790 5322 Endo 1791 Fujisawa, Kanagawa 252-0882 1792 Japan 1794 Email: rdv@sfc.wide.ad.jp 1796 Bruno Rijsman 1797 Individual 1799 Email: brunorijsman@gmail.com 1800 Angela Sara Cacciapuoti 1801 University of Naples Federico II 1802 Department of Electrical Engineering and Information Technologies 1803 Claudio 21 1804 Naples 80125 1805 Italy 1807 Email: angelasara.cacciapuoti@unina.it 1809 Marcello Caleffi 1810 University of Naples Federico II 1811 Department of Electrical Engineering and Information Technologies 1812 Claudio 21 1813 Naples 80125 1814 Italy 1816 Email: marcello.caleffi@unina.it 1818 Shota Nagayama 1819 Mercari, Inc. 1820 Roppongi Hills Mori Tower 18F 1821 6-10-1 Roppongi, Minato-ku 1822 Tokyo 106-6118 1823 Japan 1825 Email: shota.nagayama@mercari.com