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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for intended status: Informational ---------------------------------------------------------------------------- == Outdated reference: A later version (-19) exists of draft-irtf-qirg-quantum-internet-use-cases-01 Summary: 0 errors (**), 0 flaws (~~), 2 warnings (==), 1 comment (--).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: January 13, 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 July 12, 2020 16 Architectural Principles for a Quantum Internet 17 draft-irtf-qirg-principles-04 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 as the physical nature of the communication 25 is fundamentally different. The first realisations of quantum 26 networks are imminent, but there is no practical proposal for how to 27 organise, utilise, and manage such networks. In this memo, we 28 attempt to lay down the framework and introduce some basic 29 architectural principles for a quantum internet. This is intended 30 for general guidance and general interest, but also to provide a 31 foundation for discussion between physicists and network specialists. 33 Status of This Memo 35 This Internet-Draft is submitted in full conformance with the 36 provisions of BCP 78 and BCP 79. 38 Internet-Drafts are working documents of the Internet Engineering 39 Task Force (IETF). Note that other groups may also distribute 40 working documents as Internet-Drafts. The list of current Internet- 41 Drafts is at https://datatracker.ietf.org/drafts/current/. 43 Internet-Drafts are draft documents valid for a maximum of six months 44 and may be updated, replaced, or obsoleted by other documents at any 45 time. It is inappropriate to use Internet-Drafts as reference 46 material or to cite them other than as "work in progress." 48 This Internet-Draft will expire on January 13, 2021. 50 Copyright Notice 52 Copyright (c) 2020 IETF Trust and the persons identified as the 53 document authors. All rights reserved. 55 This document is subject to BCP 78 and the IETF Trust's Legal 56 Provisions Relating to IETF Documents 57 (https://trustee.ietf.org/license-info) in effect on the date of 58 publication of this document. Please review these documents 59 carefully, as they describe your rights and restrictions with respect 60 to this document. Code Components extracted from this document must 61 include Simplified BSD License text as described in Section 4.e of 62 the Trust Legal Provisions and are provided without warranty as 63 described in the Simplified BSD License. 65 Table of Contents 67 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 68 2. Quantum information . . . . . . . . . . . . . . . . . . . . . 4 69 2.1. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 4 70 2.2. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 5 71 3. Entanglement as the fundamental resource . . . . . . . . . . 6 72 4. Achieving quantum connectivity . . . . . . . . . . . . . . . 7 73 4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 8 74 4.1.1. The measurement problem . . . . . . . . . . . . . . . 8 75 4.1.2. No-cloning theorem . . . . . . . . . . . . . . . . . 8 76 4.1.3. Fidelity . . . . . . . . . . . . . . . . . . . . . . 8 77 4.1.4. Inadequacy of direct transmission . . . . . . . . . . 9 78 4.2. Bell pairs . . . . . . . . . . . . . . . . . . . . . . . 9 79 4.3. Teleportation . . . . . . . . . . . . . . . . . . . . . . 10 80 4.4. The life cycle of entanglement . . . . . . . . . . . . . 11 81 4.4.1. Elementary link generation . . . . . . . . . . . . . 11 82 4.4.2. Entanglement swapping . . . . . . . . . . . . . . . . 12 83 4.4.3. Error Management . . . . . . . . . . . . . . . . . . 13 84 4.4.4. Delivery . . . . . . . . . . . . . . . . . . . . . . 16 85 5. Architecture of a quantum internet . . . . . . . . . . . . . 16 86 5.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 16 87 5.2. Classical communication . . . . . . . . . . . . . . . . . 18 88 5.3. Abstract model of the network . . . . . . . . . . . . . . 19 89 5.3.1. Elements of a quantum network . . . . . . . . . . . . 19 90 5.3.2. Putting it all together . . . . . . . . . . . . . . . 20 91 5.4. Network boundaries . . . . . . . . . . . . . . . . . . . 21 92 5.4.1. Boundaries between different physical architectures . 21 93 5.4.2. Boundaries between different administrative regions . 21 94 5.4.3. Boundaries between different error management schemes 22 95 5.5. Physical constraints . . . . . . . . . . . . . . . . . . 22 96 5.5.1. Memory lifetimes . . . . . . . . . . . . . . . . . . 22 97 5.5.2. Rates . . . . . . . . . . . . . . . . . . . . . . . . 22 98 5.5.3. Communication qubits . . . . . . . . . . . . . . . . 23 99 5.5.4. Homogeneity . . . . . . . . . . . . . . . . . . . . . 23 100 6. Architectural principles . . . . . . . . . . . . . . . . . . 23 101 6.1. Goals of a quantum internet . . . . . . . . . . . . . . . 24 102 6.2. The principles of a quantum internet . . . . . . . . . . 26 103 7. Comparison with classical networks . . . . . . . . . . . . . 28 104 8. Security Considerations . . . . . . . . . . . . . . . . . . . 30 105 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 30 106 10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 30 107 11. Informative References . . . . . . . . . . . . . . . . . . . 31 108 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 33 110 1. Introduction 112 Quantum networks are distributed systems of quantum devices that 113 utilise fundamental quantum mechanical phenomena such as 114 superposition, entanglement, and quantum measurement to achieve 115 capabilities beyond what is possible with non-quantum (classical) 116 networks. Depending on the stage of a quantum network [8] such 117 devices may be simple photonic devices capable of preparing and 118 measuring only one quantum bit (qubit) at a time, all the way to 119 large-scale quantum computers of the future. A quantum network is 120 not meant to replace classical networks, but rather form an overall 121 hybrid classical quantum network supporting new capabilities which 122 are otherwise impossible to realise. 124 This new networking paradigm offers promise for a range of new 125 applications such as secure communications [3] [4], distributed 126 quantum computation [5], or quantum-enhanced measurement networks 127 [6]. The field of quantum communication has been a subject of active 128 research for many years and the most well-known application of 129 quantum communication, quantum key distribution (QKD) for secure 130 communications, has already been deployed at short (roughly 100km) 131 distances. 133 Fully quantum networks capable of transmitting and managing entangled 134 quantum states in order to send, receive, and manipulate distributed 135 quantum information are now imminent [7] [8]. Whilst a lot of effort 136 has gone into physically realising and connecting such devices, and 137 making improvements to their speed and error tolerance, there are no 138 worked out proposals for how to run these networks. To draw an 139 analogy with a classical network, we are at a stage where we can 140 start to physically connect our devices and send data, but all 141 sending, receiving, buffer management, connection synchronisation, 142 and so on, must be managed by the application itself at a level below 143 convential assembly language, where no common interfaces yet exist. 144 Furthermore, whilst physical mechanisms for transmitting quantum 145 states exist, there are no robust protocols for managing such 146 transmissions. 148 2. Quantum information 150 In order to understand the framework for quantum networking, a basic 151 understanding of quantum information is necessary. The following 152 sections aim to introduce the bare minimum necessary to understand 153 the principles of operation of a quantum network. This exposition 154 was written with a classical networking audience in mind. It is 155 assumed that the reader has never before been exposed to any quantum 156 physics. We refer to e.g. [15] [16] for an in-depth introduction to 157 quantum information. 159 2.1. Qubit 161 The differences between quantum computation and classical computation 162 begin at the bit-level. A classical computer operates on the binary 163 alphabet { 0, 1 }. A quantum bit, a qubit, exists over the same 164 binary space, but unlike the classical bit, it can exist in a 165 superposition of the two possibilities: 167 a |0> + b |1>, 169 where |X> is Dirac's ket notation for a quantum state, here the 170 binary 0 and 1, and the coefficients a and b are complex numbers 171 called probability amplitudes. Physically, such a state can be 172 realised using a variety of different technologies such as electron 173 spin, photon polarisation, atomic energy levels, and so on. 175 Upon measurement, the qubit loses its superposition and irreversibly 176 collapses into one of the two basis states, either |0> or |1>. Which 177 of the two states it ends up in is not deterministic, but it can be 178 determined from the readout of the measurement, a classical bit, 0 or 179 1 respectively. The probability of measuring the state in the |0> 180 state is |a|^2 and similarly the probability of measuring the state 181 in the |1> state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness 182 is not due to our ignorance of the underlying mechanisms, but rather 183 it is a fundamental feature of a quantum mechanical system [9]. 185 The superposition property plays an important role in fundamental 186 gate operations on qubits. Since a qubit can exist in a 187 superposition of its basis states, the elementary quantum gates are 188 able to act on all states of the superposition at the same time. For 189 example, consider the NOT gate: 191 NOT (a |0> + b |1>) -> a |1> + b |0>. 193 2.2. Multiple qubits 195 When multiple qubits are combined in a single quantum state the space 196 of possible states grows exponentially and all these states can 197 coexist in a superposition. For example, the general form of a two- 198 qubit register is 200 a |00> + b |01> + c |10> + d |11> 202 where the coefficients have the same probability amplitude 203 interpretation as for the single qubit state. Each state represents 204 a possible outcome of a measurement of the two-qubit register. For 205 example, |01> denotes a state in which the first qubit is in the 206 state |0> and the second is in the state |1>. 208 Performing single qubit gates affects the relevant qubit in each of 209 the superposition states. Similarly, two-qubit gates also act on all 210 the relevant superposition states, but their outcome is far more 211 interesting. 213 Consider a two-qubit register where the first qubit is in the 214 superposed state (|0> + |1>)/sqrt(2) and the other is in the 215 state |0>. This combined state can be written as: 217 (|0> + |1>)/sqrt(2) x |0> = (|00> + |10>)/sqrt(2), 219 where x denotes a tensor product (the mathematical mechanism for 220 combining quantum states together). Let us now consider the two- 221 qubit controlled-NOT, or CNOT, gate. The CNOT gate takes as input 222 two qubits, a control and target, and applies the NOT gate to the 223 target if the control qubit is set. The truth table looks like 225 +----+-----+ 226 | IN | OUT | 227 +----+-----+ 228 | 00 | 00 | 229 | 01 | 01 | 230 | 10 | 11 | 231 | 11 | 10 | 232 +----+-----+ 234 Now, consider performing a CNOT gate on the state with the first 235 qubit being the control. We apply a two-qubit gate on all the 236 superposition states: 238 CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2). 240 What is so interesting about this two-qubit gate operation? The 241 final state is *entangled*. There is no possible way of representing 242 that quantum state as a product of two individual qubits; they are no 243 longer independent and the behaviour of either qubit cannot be fully 244 described without accounting for the other qubit. The states of the 245 two individual qubits are now correlated beyond what is possible to 246 achieve classically. Neither qubit is in a definite |0> or |1> 247 state, but if we perform a measurement on either one, the outcome of 248 the partner qubit will *always* yield the exact same outcome. The 249 final state, whether it's |00> or |11>, is fundamentally random as 250 before, but the states of the two qubits following a measurement will 251 always be identical. 253 Once a measurement is performed, the two qubits are once again 254 independent. The final state is either |00> or |11> and both of 255 these states can be trivially decomposed into a product of two 256 individual qubits. The entanglement has been consumed and the 257 entangled state must be prepared again. 259 3. Entanglement as the fundamental resource 261 Entanglement is the fundamental building block of quantum networks. 262 Consider the state from the previous section: 264 (|00> + |11>)/sqrt(2). 266 Neither of the two qubits is in a definite |0> or |1> state and we 267 need to know the state of the entire register to be able to fully 268 describe the behaviour of the two qubits. 270 Entangled qubits have interesting non-local properties. Consider 271 sending one of the qubits to another device. This device could in 272 principle be anywhere: on the other side of the room, in a different 273 country, or even on a different planet. Provided negligible noise 274 has been introduced, the two qubits will forever remain in the 275 entangled state until a measurement is performed. The physical 276 distance does not matter at all for entanglement. 278 This lies at the heart of quantum networking, because it is possible 279 to leverage the non-classical correlations provided by entanglement 280 in order to design completely new types of application protocols that 281 are not possible to achieve with just classical communication. 282 Examples of such applications are quantum cryptography, blind quantum 283 computation, or distributed quantum computation. 285 Entanglement has two very special features from which one can derive 286 some intuition about the types of applications enabled by a quantum 287 network. 289 The first stems from the fact that entanglement enables stronger than 290 classical correlations, leading to opportunities for tasks that 291 require coordination. As a trivial example, consider the problem of 292 consensus between two nodes who want to agree on the value of a 293 single bit. They can use the quantum network to prepare the state 294 (|00> + |11>)/sqrt(2) with each node holding one of the two qubits. 295 Once either of the two nodes performs a measurement, the state of the 296 two qubits collapses to either |00> or |11>, so whilst the outcome is 297 random and does not exist before measurement, the two nodes will 298 always measure the same value. We can also build the more general 299 multi-qubit state (|00...> + |11...>)/sqrt(2) and perform the same 300 algorithm between an arbitrary number of nodes. These stronger than 301 classical correlations generalise to more complicated measurement 302 schemes as well. 304 The second feature of entanglement is that it cannot be shared, in 305 the sense that if two qubits are maximally entangled with each other, 306 then it is physically impossible for any other system to have any 307 share of this entanglement. Hence, entanglement forms a sort of 308 private and inherently untappable connection between two nodes once 309 established. 311 Entanglement is created through local interactions between two qubits 312 or as a product of the way the qubits were created (e.g. entangled 313 photon pairs). To create a distributed entangled state, one can then 314 physically send one of the qubits to a remote node. It is also 315 possible to directly entangle qubits that are physically separated, 316 but this still requires local interactions between some other qubits 317 that the separated qubits are initially entangled with. Therefore, 318 it is the transmission of qubits that draws the line between a 319 genuine quantum network and a collection of quantum computers 320 connected over a classical network. 322 A quantum network is defined as a collection of nodes that is able to 323 exchange qubits and distribute entangled states amongst themselves. 324 A quantum node that is able only to communicate classically with 325 another quantum node is not a member of a quantum network. 327 More complex services and applications can be built on top of 328 entangled states distributed by the network, see e.g. [8]> 330 4. Achieving quantum connectivity 332 This section explains the meaning of quantum connectivity and the 333 necessary physical processes at an abstract level. 335 4.1. Challenges 337 A quantum network cannot be built by simply extrapolating all the 338 classical models to their quantum analogues. Sending qubits over a 339 wire like we send classical bits is simply not as easy to do. There 340 are several technological as well as fundamental challenges that make 341 classical approaches unsuitable in a quantum context. 343 4.1.1. The measurement problem 345 In classical computers and networks we can read out the bits stored 346 in memory at any time. This is helpful for a variety of purposes 347 such as copying, error detection and correction, and so on. This is 348 not possible with qubits. 350 A measurement of a qubit's state will destroy its superposition and 351 with it any entanglement it may have been part of. Once a qubit is 352 being processed, it cannot be read out until a suitable point in the 353 computation, determined by the protocol handling the qubit, has been 354 reached. Therefore, we cannot use the same methods known from 355 classical computing for the purposes of error detection and 356 correction. Nevertheless, quantum error detection and correction 357 schemes exist that take this problem into account and how a network 358 chooses to manage errors will have an impact on its architecture. 360 4.1.2. No-cloning theorem 362 Since directly reading the state of a qubit is not possible, one 363 could ask the question if we can simply copy a qubit without looking 364 at it. Unfortunately, this is fundamentally not possible in quantum 365 mechanics. 367 The no-cloning theorem states that it is impossible to create an 368 identical copy of an arbitrary, unknown quantum state. Therefore, it 369 is also impossible to use the same mechanisms that worked for 370 classical networks for signal amplification, retransmission, and so 371 on as they all rely on the ability to copy the underlying data. 372 Since any physical channel will always be lossy, connecting nodes 373 within a quantum network is a challenging endeavour and its 374 architecture must at its core address this very issue. 376 4.1.3. Fidelity 378 In general, it is expected that a classical packet arrives at its 379 destination without any errors introduced by hardware noise along the 380 way. This is verified at various levels through a variety of error 381 detection and correction mechanisms. Since we cannot read or copy a 382 quantum state error detection and correction is more involved. 384 To describe the quality of a quantum state, a physical quantity 385 called fidelity is used. Fidelity takes a value between 0 and 1 -- 386 higher is better, and less than 0.5 means the state is unusable. It 387 measures how close a quantum state is to the state we have tried to 388 create. It expresses the probability that one state will pass a test 389 to identify as the other. Fidelity is an important property of a 390 quantum system that allows us to quantify how much a particular state 391 has been affected by noise from various sources (gate errors, channel 392 losses, environment noise). 394 Interestingly, quantum applications do not need perfect fidelity to 395 be able to execute -- as long as the fidelity is above some 396 application-specific threshold, they will simply operate at lower 397 rates. Therefore, rather than trying to ensure that we always 398 deliver perfect states (a technologically challenging task) 399 applications will specify a minimum threshold for the fidelity and 400 the network will try its best to deliver it. A higher fidelity can 401 be achieved by either having hardware produce states of better 402 fidelity (sometimes one can sacrifice rate for higher fidelity) or by 403 employing quantum error detection and correction mechanisms. 405 4.1.4. Inadequacy of direct transmission 407 Conceptually, the most straightforward way to distribute an entangled 408 state is to simply transmit one of the qubits directly to the other 409 end across a series of nodes while performing sufficient forward 410 quantum error correction Section 4.4.3.2 to bring losses down to an 411 acceptable level. Despite the no-cloning theorem and the inability 412 to directly measure a quantum state, error-correcting mechanisms for 413 quantum communication exist [10]. However, quantum error correction 414 makes very high demands on both resources (physical qubits needed) 415 and their initial fidelity. Implementation is very challenging and 416 quantum error correction is not expected to be used until later 417 generations of quantum networks. 419 An alternative relies on the observation that we do not need to be 420 able to distribute any arbitrary entangled quantum state. We only 421 need to be able to distribute any one of what are known as the Bell 422 pair states[18]. 424 4.2. Bell pairs 426 Bell pair states are the entangled two-qubit states: 428 |00> + |11>, 429 |00> - |11>, 430 |01> + |10>, 431 |01> - |10>, 432 where the constant 1/sqrt(2) normalisation factor has been ignored 433 for clarity. Any of the four Bell pair states above will do, as it 434 is possible to transform any Bell pair into another Bell pair with 435 local operations performed on only one of the qubits. When each 436 qubit in a Bell pair is held by a separate node, either can apply a 437 series of single qubit gates to their qubit alone in order to 438 transform the state between the different variants. 440 Distributing a Bell pair between two nodes is much easier than 441 transmitting an arbitrary quantum state over a network. Since the 442 state is known, handling errors becomes easier and small-scale error- 443 correction (such as entanglement distillation discussed in a later 444 section) combined with reattempts becomes a valid strategy. 446 The reason for using Bell pairs specifically as opposed to any other 447 two-qubit state, is that they are the maximally entangled two-qubit 448 set of basis states. Maximal entanglement means that these states 449 have the strongest non-classical correlations of all possible two- 450 qubit states. Furthermore, since single-qubit local operations can 451 never increase entanglement, less entangled states would impose some 452 constraints on distributed quantum algorithms. This makes Bell pairs 453 particularly useful as a generic building block for distributed 454 quantum applications. 456 4.3. Teleportation 458 The observation that we only need to be able to distribute Bell pairs 459 relies on the fact that this enables the distribution of any other 460 arbitrary entangled state. This can be achieved via quantum state 461 teleportation. Quantum state teleportation consumes an unknown 462 quantum state that we want to transmit and recreates it at the 463 desired destination. This does not violate the no-cloning theorem as 464 the original state is destroyed in the process. 466 To achieve this, an entangled pair needs to be distributed between 467 the source and destination before teleportation commences. The 468 source then entangles the transmission qubit with its end of the pair 469 and performs a read out of the two qubits (the sum of these 470 operations is called a Bell state measurement). This consumes the 471 Bell pair's entanglement, turning the source and destination qubits 472 into independent states. The measurements yields two classical bits 473 which the source sends to the destination over a classical channel. 474 Based on the value of the received two classical bits, the 475 destination performs one of four possible corrections (called the 476 Pauli corrections) on its end of the pair which turns it into the 477 unknown quantum state that we wanted to transmit. 479 The unknown quantum state that was transmitted was never fed into the 480 network itself. Therefore, the network needs to only be able to 481 reliably produce Bell pairs between any two nodes in the network. 482 Thus, a key difference between a classical and quantum data planes is 483 that a classical one carries user data, but a quantum data plate 484 provides the resources for the user to transmit user data themselves 485 without further involvement of the network. 487 4.4. The life cycle of entanglement 489 Reducing the problem of quantum connectivity to one of generating a 490 Bell pair has facilitated the problem, but it has not solved it. In 491 this section, we discuss how these entangled pairs are generated in 492 the first place, and how their two qubits are delivered to the end- 493 points. 495 4.4.1. Elementary link generation 497 In a quantum network, entanglement is always first generated locally 498 (at a node or an auxiliary element) followed by a movement of one or 499 both of the entangled qubits across the link through quantum 500 channels. In this context, photons (particles of light) are the 501 natural candidate for entanglement carriers, called flying qubits. 502 The rationale for this choice is related to the advantages provided 503 by photons such as moderate interaction with the environment leading 504 to moderate decoherence, convenient control with standard optical 505 components, and high-speed, low-loss transmissions. However, since 506 photons cannot be stored, a transducer must transfer the flying 507 qubit's state to a qubit suitable for information processing and/or 508 storage (often referred to as a matter qubit). 510 Since this process may fail, in order to generate and store 511 entanglement efficiently, we must be able to distinguish successful 512 attempts from failures. Entanglement generation schemes that are 513 able to announce successful generation are called heralded 514 entanglement generation schemes. 516 There exist three basic schemes for heralded entanglement generation 517 on a link through coordinated action of the two nodes at the two ends 518 of the link [19]: 520 o "At mid-point": in this scheme an entangled photon pair source 521 sitting midway between the two nodes with matter qubits sends an 522 entangled photon through a quantum channel to each of the nodes. 523 There, transducers are invoked to transfer the entanglement from 524 the flying qubits to the matter qubits. In this scheme, the 525 transducers know if the transfers succeeded and are able to herald 526 successful entanglement generation via a message exchange over the 527 classical channel. 529 o "At source": in this scheme one of the two nodes sends a flying 530 qubit that is entangled with one of its matter qubits. A 531 transducer at the other end of the link will transfer the 532 entanglement from the flying qubit to one of its matter qubits. 533 Just like in the previous scheme, the transducer knows if its 534 transfer succeeded and is able to herald successful entanglement 535 generation with a classical message sent to the other node. 537 o "At both end-points": in this scheme both nodes send a flying 538 qubit that is entangled with one of their matter qubits. A 539 detector somewhere in between the nodes performs a joint 540 measurement on the two qubits, which stochastically projects the 541 remote matter qubits into an entangled quantum state. The 542 detector knows if the entanglement succeeded and is able to herald 543 successful entanglement generation by sending a message to each 544 node over the classical channel. 546 The "mid-point source" scheme is more robust to photon loss, but in 547 the other schemes the nodes retain greater control over the entangled 548 pair generation. 550 Note that whilst photons travel in a particular direction through the 551 quantum channel the resulting entangled pair of qubits does not have 552 a direction associated with it. Physically, there is no upstream or 553 downstream end of the pair. 555 4.4.2. Entanglement swapping 557 The problem with generating entangled pairs directly across a link is 558 that efficiency decreases with channel length. Beyond a few 10s of 559 kms in optical fibre or 1000 kms in free space (via satellite) the 560 rate is effectively zero and due to the no-cloning theorem we cannot 561 simply amplify the signal. The solution is entanglement swapping. 563 A Bell pair between any two nodes in the network can be constructed 564 by combining the pairs generated along each individual link on a path 565 between the two end-points. Each node along the path can consume the 566 two pairs on the two links that it is connected to in order to 567 produce a new entangled pair between the two remote ends. This 568 process is known as entanglement swapping. Pictorially it can be 569 represented as follows: 571 +---------+ +---------+ +---------+ 572 | A | | B | | C | 573 | |------| |------| | 574 | X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 | 575 +---------+ +---------+ +---------+ 577 where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2 578 are the qubits of entangled pair Y. The entanglement is denoted with 579 ~~. In the diagram above, nodes A and B share the pair X and nodes B 580 and C share the pair Y, but we want entanglement between A and C. 582 To achieve this goal, we simply teleport the qubit X2 using the pair 583 Y. This requires node B to perform a Bell state measurement on the 584 qubits X2 and Y1 which result in the destruction of the entanglement 585 between Y1 and Y2. However, X2 is recreated in Y2's place, carrying 586 with it its entanglement with X1. The end-result is shown below: 588 +---------+ +---------+ +---------+ 589 | A | | B | | C | 590 | |------| |------| | 591 | X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 | 592 +---------+ +---------+ +---------+ 594 Depending on the needs of the network and/or application, a final 595 Pauli correction at the recipient node may not be necessary since the 596 result of this operation is also a Bell pair. However, the two 597 classical bits that form the read out from the measurement at node B 598 must still be communicated, because they carry information about 599 which of the four Bell pairs was actually produced. If a correction 600 is not performed, the recipient must be informed which Bell pair was 601 received. 603 This process of teleporting Bell pairs using other entangled pairs is 604 called entanglement swapping. Quantum nodes that create long- 605 distance entangled pairs via entanglement swapping are called quantum 606 repeaters in academic literature [18] and we will use the same 607 terminology in this memo. 609 4.4.3. Error Management 611 4.4.3.1. Distillation 613 Neither the generation of Bell pairs nor the swapping operations are 614 noiseless operations. Therefore, with each link and each swap the 615 fidelity of the state degrades. However, it is possible to create 616 higher fidelity Bell pair states from two or more lower fidelity 617 pairs through a process called distillation (sometimes also referred 618 to as purification). 620 To distil a quantum state, a second (and sometimes third) quantum 621 state is used as a "test tool" to test a proposition about the first 622 state, e.g., "the parity of the two qubits in the first state is 623 even." When the test succeeds, confidence in the state is improved, 624 and thus the fidelity is improved. The test tool states are 625 destroyed in the process, so resource demands increase substantially 626 when distillation is used. When the test fails, the tested state 627 must also be discarded. Distillation makes low demands on fidelity 628 and resources compared to quantum error correction, but distributed 629 protocols incur round-trip delays due to classical communication 630 [17]. 632 4.4.3.2. Quantum Error Correction 634 Just like classical error correction, quantum error correction (QEC) 635 encodes logical qubits using several physical (raw) qubits to protect 636 them from errors described in Section 4.1.3. Furthermore, similarly 637 to its classical counterpart, QEC can not only correct state errors 638 but also account for lost qubits. Additionally, if all physical 639 qubits which encode a logical qubit are located at the same node, the 640 correction procedure can be executed locally, even if the logical 641 qubit is entangled with remote qubits. 643 Although QEC was originally a scheme proposed to protect a qubit from 644 noise, QEC can also be applied to entanglement distillation. Such 645 QEC-applied distillation is cost-effective but requires a higher base 646 fidelity. 648 One big difference from classical error correction is the code-rate. 649 QEC encodes a single logical qubit using many physical qubits. 651 4.4.3.3. Error management schemes 653 Quantum networks have been categorized into three "generations" based 654 on the error management scheme they employ[10]. Note that these 655 "generations" are more like categories; they do not necessarily imply 656 a time progression and do not obsolete each other, though the later 657 generations do require more advanced technologies. Which generation 658 is used depends on the hardware platform and network design choices. 660 Table Table 1 summarises the generations. 662 +-----------+-----------------+------------------------+------------+ 663 | | First | Second generation | Third | 664 | | generation | | generation | 665 +-----------+-----------------+------------------------+------------+ 666 | Loss | Heralded | Heralded entanglement | Quantum | 667 | tolerance | entanglement | generation (bi- | Error | 668 | | generation (bi- | directional classical | Correction | 669 | | directional | signaling) | (no | 670 | | classical | | classical | 671 | | signaling) | | signaling) | 672 | | | | | 673 | Error | Entanglement | Entanglement | Quantum | 674 | tolerance | distillation | distillation (uni- | Error | 675 | | (bi-directional | directional classical | Correction | 676 | | classical | signaling) or | (no | 677 | | signaling) | Quantum Error | classical | 678 | | | Correction (no | signaling) | 679 | | | classical signaling) | | 680 +-----------+-----------------+------------------------+------------+ 682 Table 1: Classical signaling and generations 684 Generations are defined by the directions of classical signalling 685 required in their distributed protocols for loss tolerance and error 686 tolerance. Classical signalling carries the classical bits and 687 incurs round-trip delays described in Section 4.4.3.1, hence they 688 affect the performance of quantum networks, especially as the 689 distance between the communicating nodes increases. 691 Loss tolerance is about tolerating qubit transmission losses between 692 nodes. Heralded entanglement generation, as described in 693 Section 4.4.1, confirms the receipt of an entangled qubit using a 694 heralding signal. A pair of directly connected quantum nodes 695 repeatedly attempt to generate an entangled pair until the a 696 heralding signal is received. As described in Section 4.4.3.2, QEC 697 can be applied to complement lost qubits eliminating the need for re- 698 attempts. Furthermore, since the correction procedure is composed of 699 local operations, it does not require a heralding signal. However, 700 it is feasible only when the photon loss rate is less than 0.5. 702 Error tolerance is about tolerating quantum state errors. 703 Entanglement distillation is the easiest mechanism for improved error 704 tolerance to implement, but it incurs round-trip delays due the 705 requirement for bi-directional classical signalling. The 706 alternative, QEC, is able to correct state errors locally so that it 707 does not need any classical signalling between the quantum nodes. In 708 between these two extremes, there is also QEC-applied distillation, 709 which requires uni-directional classical signalling. 711 The three "generations" summarised: 713 1. First generation quantum networks use heralding for loss 714 tolerance and entanglement distillation for error tolerance. 715 These networks can be implemented using only small, shallow 716 quantum circuits at each node. 718 2. Second generation quantum networks are empowered by QEC codes for 719 error tolerance. At first, QEC will be applied to entanglement 720 distillation only which requires uni-directional classical 721 signalling. Later, QEC codes will be used to create logical Bell 722 pairs which no longer require any classical signalling for the 723 purposes of error tolerance. Heralding is still used to 724 compensate for transmission losses. 726 3. Third generation quantum networks directly transmit QEC encoded 727 qubits to adjacent nodes, as discussed in Section 4.1.4. 728 Elementary link Bell pairs can now be created without heralding 729 or any other classical signalling. Furthermore, this also 730 enables direct transmission architectures in which qubits are 731 forwarded end-to-end like classical packets rather than relying 732 on Bell pairs and entanglement swapping. 734 4.4.4. Delivery 736 Eventually, the Bell pairs must be delivered to an application (or 737 higher layer protocol) at the two end-nodes. A detailed list of such 738 requirements is beyond the scope of this memo. At minimum, the end- 739 nodes require information to map a particular Bell pair to the qubit 740 in their local memory that is part of this entangled pair. 742 5. Architecture of a quantum internet 744 It is evident from the previous sections that the fundamental service 745 provided by a quantum network significantly differs from that of a 746 classical network. Therefore, it is not surprising that the 747 architecture of a quantum internet will itself be very different from 748 that of the classical Internet. 750 5.1. Challenges 752 This subsection covers the major fundamental challenges building 753 quantum networks. Here, we only describe the fundamental 754 differences. Technological limitations are described later. 756 1. Bell pairs are not equivalent to payload carrying packets. 758 In most classical networks, including Ethernet, Internet Protocol 759 (IP), and Multi-Protocol Label Switching (MPLS) networks, user 760 data is grouped into packets. In addition to the user data, each 761 packet also contains a series of headers which contain the 762 control information that lets routers and switches forward it 763 towards its destination. Packets are the fundamental unit in a 764 classical network. 766 In a quantum network, the entangled pairs of qubits are the basic 767 unit of networking. These qubits themselves do not carry any 768 headers. Therefore, quantum networks will have to send all 769 control information via separate classical channels which the 770 repeaters will have to correlate with the qubits stored in their 771 memory. 773 2. "Store and forward" vs "store and swap" quantum networks. 775 As described in Section 4.4.1, quantum links provide Bell pairs 776 that are undirected network resources, in contrast to directed 777 frames of classical networks. This phenomenological distinction 778 leads to architectural differences between quantum networks and 779 classical networks. Quantum networks combine multiple elementary 780 link Bell pairs together to create one an end-to-end Bell pair, 781 whereas classical networks deliver messages from one end to the 782 other end hop by hop. 784 Classical networks receive data on one interface, store it in 785 local buffers, then forward the data to another appropriate 786 interface. Quantum networks store Bell pairs and then execute 787 entanglement swapping instead of forwarding in the data plane. 788 Such quantum networks are "store and swap" networks. In "store 789 and swap" networks, we do not need to care about the order in 790 which the Bell pairs were generated since they are undirected. 791 This distinction makes control algorithms and optimisation of 792 quantum networks different from classical ones. Note that third 793 generation quantum networks, as described in Section 4.4.1, will 794 be able to support a "store and forward" architecture in addition 795 to "store and swap". 797 3. An entangled pair is only useful if the locations of both qubits 798 are known. 800 A classical network packet logically exists only at one location 801 at any point in time. If a packet is modified in some way, 802 whether headers or payload, this information does not need to be 803 conveyed to anybody else in the network. The packet can be 804 simply forwarded as before. 806 In contrast, entanglement is a phenomenon in which two or more 807 qubits exist in a physically distributed state. Operations on 808 one of the qubits change the mutual state of the pair. Since the 809 owner of a particular qubit cannot just read out its state, it 810 must coordinate all its actions with the owner of the pair's 811 other qubit. Therefore, the owner of any qubit that is part of 812 an entangled pair must know the location of its counterpart. 813 Location, in this context, need not be the explicit spatial 814 location. A relevant pair identifier, a means of communication 815 between the pair owners, and an association between the pair ID 816 and the individual qubits is sufficient. 818 4. Generating entanglement requires temporary state. 820 Packet forwarding in a classical network is largely a stateless 821 operation. When a packet is received, the router looks up its 822 forwarding table and sends the packet out of the appropriate 823 output. There is no need to keep any memory of the packet any 824 more. 826 A quantum node must be able to make decisions about qubits that 827 it receives and is holding in its memory. Since qubits do not 828 carry headers, the receipt of an entangled pair conveys no 829 control information based on which the repeater can make a 830 decision. The relevant control information will arrive 831 separately over a classical channel. This implies that a 832 repeater must store temporary state as the control information 833 and the qubit it pertains to will, in general, not arrive at the 834 same time. 836 5.2. Classical communication 838 In this memo we have already covered two different roles that 839 classical communication must perform: 841 o communicate classical bits of information as part of distributed 842 protocols such as entanglement swapping and teleportation, 844 o communicate control information within a network, including both 845 background protocols such as routing as well as signalling 846 protocols to set up end-to-end entanglement generation. 848 Classical communication is a crucial building block of any quantum 849 network. All nodes in a quantum network are assumed to have 850 classical connectivity with each other (within typical administrative 851 domain limts). Therefore, quantum routers will need to manage two 852 data planes in parallel, a classical one and a quantum one. 853 Additionally, a node must be able to correlate information between 854 the two planes so that the control information received on a 855 classical channel can be applied to the qubits managed by the quantum 856 data plane. 858 5.3. Abstract model of the network 860 5.3.1. Elements of a quantum network 862 We have identified quantum repeaters as the core building block of a 863 quantum network. However, a quantum repeater will have to do more 864 than just entanglement swapping in a functional quantum network. Its 865 key responsibilities will include: 867 1. Creating link-local entanglement between neighbouring nodes. 869 2. Extending entanglement from link-local pairs to long-range pairs 870 through entanglement swapping. 872 3. Performing distillation to manage the fidelity of the produced 873 pairs. 875 4. Participating in the management of the network (routing, etc.). 877 Not all quantum repeaters in the network will be the same; here we 878 break them down further: 880 o Quantum routers (controllable quantum nodes) - A quantum router is 881 a quantum repeater with a control plane that participates in the 882 management of the network and will make decisions about which 883 qubits to swap to generate the requested end-to-end pairs. 885 o Automated quantum nodes - An automated quantum node is a data 886 plane only quantum repeater that does not participate in network 887 management. Since the no-cloning theorem precludes the use of 888 amplification, long-range links will be established by chaining 889 multiple such automated nodes together. 891 o End-nodes - End-nodes in a quantum network must be able to receive 892 and handle an entangled pair, but they do not need to be able to 893 perform an entanglement swap (and thus are not necessarily quantum 894 repeaters). End-nodes are also not required to have any quantum 895 memory as certain quantum applications can be realised by having 896 the end-node measure its qubit as soon as it is received. 898 o Non-quantum nodes - Not all nodes in a quantum network need to 899 have a quantum data plane. A non-quantum node is any device that 900 can handle classical network traffic. 902 Additionally, we need to identify two kinds of links that will be 903 used in a quantum network: 905 o Quantum links - A quantum link is a link which can be used to 906 generate an entangled pair between two directly connected quantum 907 repeaters. It may include a dedicated classical channel that is 908 to be used solely for the purpose of coordinating the entanglement 909 generation on this quantum link. 911 o Classical links - A classical link is a link between any node in 912 the network that is capable of carrying classical network traffic. 914 5.3.2. Putting it all together 916 A two-hop path in a generic quantum network can be represented as: 918 | App |-------------------CC-------------------| App | 919 || || 920 ------ ------ ------ 921 | EN |----QC & CC----| QR |----QC & CC----| EN | 922 ------ ------ ------ 924 App - user-level application 925 QR - quantum repeater 926 EN - end-node 927 QC - quantum channel 928 CC - classical channel 930 An application running on two end-nodes attached to a network will at 931 some point need the network to generate entangled pairs for its use. 932 This will require negotiation between the end-nodes, because they 933 must both open a communication end-point (a quantum socket) which the 934 network can use to identify the two ends of the connection. The two 935 end-nodes use the classical connectivity available in the network to 936 achieve this goal. 938 When the network receives a request to generate end-to-end entangled 939 pairs it uses the classical communication channels to coordinate and 940 claim the resources necessary to fulfill this request. This may be 941 some combination of prior control information (e.g. routing tables) 942 and signalling protocols, but the details of how this is achieved are 943 an active research question and thus beyond the scope of this memo. 945 During or after the distribution of control information, the network 946 performs the necessary quantum operations such as generating 947 entanglement over individual links, performing entanglement swaps, 948 and further signalling to transmit the swap outcomes and other 949 control information. Since none of the entangled pairs carry any 950 user data, some of these operations can be performed before the 951 request is received in anticipation of the demand. 953 The entangled pair is delivered to the application once it is ready, 954 together with the relevant pair identifier. However, being ready 955 does not necessarily mean that all link pairs and entanglement swaps 956 are complete, as some applications can start executing on an 957 incomplete pair. In this case the remaining entanglement swaps will 958 propagate the actions across the network to the other end, sometimes 959 necessitating fixup operations at the end node. 961 5.4. Network boundaries 963 Just like classical networks, various boundaries will exist in 964 quantum networks. 966 5.4.1. Boundaries between different physical architectures 968 There are many different physical architectures for implementing 969 quantum repeater technology. The different technologies differ in 970 how they store and manipulate qubits in memory and how they generate 971 entanglement across a link with their neighbours. Different 972 architectures come with different trade-offs and thus a functional 973 network will likely consist of a mixture of different types of 974 quantum repeaters. 976 For example, architectures based on optical elements and atomic 977 ensembles are very efficient at generating entanglement, but provide 978 little control over the qubits once the pair is generated. On the 979 other hand, nitrogen-vacancy architectures offer a much greater 980 degree of control over qubits, but have a harder time generating the 981 entanglement across a link. 983 It is an open research question where exactly the boundary will lie. 984 It could be that a single quantum repeater node provides some 985 backplane connection between the architectures, but it also could be 986 that special quantum links delineate the boundary. 988 5.4.2. Boundaries between different administrative regions 990 Just like in classical networks, multiple quantum networks will 991 connect into a global quantum internet. This necessarily implies the 992 existence of borders between different administrative regions. How 993 these boundaries will be handled is also an open question and thus 994 beyond the scope of this memo. 996 5.4.3. Boundaries between different error management schemes 998 Not only are there physical differences and administrative 999 boundaries, but there are important distinctions in how errors will 1000 be managed, as described in Section 4.4.3.3, which affects the 1001 content and semantics of messages that must cross those boundaries -- 1002 both for connection setup and real-time operation. How to 1003 interconnect those schemes is also an open research question. 1005 5.5. Physical constraints 1007 The model above has effectively abstracted away the particulars of 1008 the hardware implementation. However, certain physical constraints 1009 need to be considered in order to build a practical network. Some of 1010 these are fundamental constraints and no matter how much the 1011 technology improves, they will always need to be addressed. Others 1012 are artefacts of the early stages of a new technology. Here, we 1013 consider a highly abstract scenario and refer to [8] for pointers to 1014 the physics literature. 1016 5.5.1. Memory lifetimes 1018 In addition to discrete operations being imperfect, storing a qubit 1019 in memory is also highly non-trivial. The main difficulty in 1020 achieving persistent storage is that it is extremely challenging to 1021 isolate a quantum system from the environment. The environment 1022 introduces an uncontrollable source of noise into the system which 1023 affects the fidelity of the state. This process is known as 1024 decoherence. Eventually, the state has to be discarded once its 1025 fidelity degrades too much. 1027 The memory lifetime depends on the particular physical setup, but the 1028 highest achievable values currently are on the order of seconds. 1029 These values have increased tremendously over the lifetime of the 1030 different technologies and are bound to keep increasing. However, if 1031 quantum networks are to be realised in the near future, they need to 1032 be able to handle short memory lifetimes, for example by reducing 1033 latency on critical paths. 1035 5.5.2. Rates 1037 Entanglement generation on a link between two connected nodes is not 1038 a very efficient process and it requires many attempts to succeed. A 1039 fast repetition rate for Bell pair generation is achievable, but only 1040 a small fraction will succeed. Currently, the highest achievable 1041 rates of success between nodes capable of storing the resulting 1042 qubits are on the order of 10 Hz. Combined with short memory 1043 lifetimes this leads to very tight timing windows to build up 1044 network-wide connectivity. 1046 5.5.3. Communication qubits 1048 Most physical architectures capable of storing qubits are only able 1049 to generate entanglement using only a subset of its available qubits 1050 called communication qubits. Once a Bell pair has been generated 1051 using a communication qubit, its state can be transferred into 1052 memory. This may impose additional limitations on the network. In 1053 particular if a given node has only one communication qubit it cannot 1054 simultaneously generate Bell Pairs over two links. It must generate 1055 entanglement over the links one at a time. 1057 5.5.4. Homogeneity 1059 Currently all hardware implementations are homogeneous and they do 1060 not interface with each other. In general, it is very challenging to 1061 combine different quantum information processing technologies at 1062 present. Coupling different technologies with each other is of great 1063 interest as it may help overcome the weaknesses of the different 1064 implementations, but this may take a long time to be realised with 1065 high reliability and thus is not a near-term goal. 1067 6. Architectural principles 1069 Given that the most practical way of realising quantum network 1070 connectivity is using Bell pair and entanglement swapping repeater 1071 technology, what sort of principles should guide us in assembling 1072 such networks such that they are functional, robust, efficient, and 1073 most importantly, they work? Furthermore, how do we design networks 1074 so that they work under the constraints imposed by the hardware 1075 available today, but do not impose unnecessary burdens on future 1076 technology? 1078 As this is a completely new technology that is likely to see many 1079 iterations over its lifetime, this memo must not serve as a 1080 definitive set of rules, but merely as a general set of recommended 1081 guidelines for the first generations of quantum networks based on 1082 principles and observations made by the community. The benefit of 1083 having a community built document at this early stage is that 1084 expertise in both quantum information and network architecture is 1085 needed in order to successfully build a quantum internet. 1087 6.1. Goals of a quantum internet 1089 When outlining any set of principles we must ask ourselves what goals 1090 do we want to achieve as inevitably trade-offs must be made. So what 1091 sort of goals should drive a quantum network architecture? The 1092 following list has been inspired by the history of computer 1093 networking and thus it is inevitably very similar to one that could 1094 be produced for the classical Internet [21]. However, whilst the 1095 goals may be similar the challenges involved are often fundamentally 1096 different. The list will also most likely evolve with time and the 1097 needs of its users. 1099 1. Support distributed quantum applications 1101 This goal seems trivially obvious, but makes a subtle, but 1102 important point which highlights a key difference between quantum 1103 and classical networks. Ultimately, quantum data transmission is 1104 not the goal of a quantum network - it is only one possible 1105 component of more advanced quantum application protocols. Whilst 1106 transmission certainly could be used as a building block for all 1107 quantum applications, it is not the most basic one possible. For 1108 example, QKD, the most well known quantum application protocol, 1109 only relies on the stronger-than-classical correlations and 1110 inherent secrecy of entangled Bell pairs and does not transmit 1111 arbitrary quantum states[4]. 1113 The primary purpose of a quantum internet is to support 1114 distributed quantum application protocols and it is of utmost 1115 importance that they can run well and efficiently. Thus, it is 1116 important to develop performance metrics meaningful to 1117 application to drive the development of quantum network 1118 protocols. For example, the Bell pair generation rate is 1119 meaningless if one does not also consider their fidelity. It is 1120 generally much easier to generate pairs of lower fidelity, but 1121 quantum applications may have to make multiple re-attempts or 1122 even abort if the fidelity is too low. A review of the 1123 requirements for different known quantum applications can be 1124 found in [8] and an overview of use-cases can be found in [2]. 1126 2. Support tomorrow's distributed quantum applications 1128 The only principle of the Internet that should survive 1129 indefinitely is the principle of constant change [1]. Technical 1130 change is continuous and the size and capabilities of the quantum 1131 internet will change by orders of magnitude. Therefore, it is an 1132 explicit goal that a quantum internet architecture be able to 1133 embrace this change. We have the benefit of having been witness 1134 to the evolution of the classical Internet over several decades 1135 and seen what worked and what did not. It is vital for a quantum 1136 internet to avoid the need for flag days (e.g. NCP to TCP/IP) or 1137 upgrades that take decades to roll out (e.g. IPv4 to IPv6). 1138 Therefore, it is important that any proposed architecture for 1139 general purpose quantum repeater networks can integrate new 1140 devices and solutions as they become available. It should not be 1141 constrained due to considerations for early-stage hardware and 1142 applications. For example, it is already possible to run QKD 1143 efficiently on metropolitan scales and such networks are already 1144 commercially available. However, they are not based on quantum 1145 repeaters and thus will not be able to easily transition to more 1146 sophisticated applications. 1148 3. Support heterogeneity 1150 There are multiple proposals for realising practical quantum 1151 repeater hardware and they all have their advantages and 1152 disadvantages. Some may offer higher Bell pair generation rates 1153 on individual links at the cost of more difficult entanglement 1154 swap operations. Other platforms may be good all around, but are 1155 more difficult to build. 1157 In addition to physical boundaries, there may be distinctions in 1158 how errors are managed Section 4.4.3.3. These difference will 1159 affect the content and semantics of messages that cross these 1160 boundaries -- both for connection setup and real-time operation. 1162 The optimal network configuration will likely leverage the 1163 advantages of multiple platforms to optimise the provided 1164 service. Therefore, it is an explicit goal to incorporate varied 1165 hardware and technology support from the beginning. 1167 4. Ensure security at the network level 1169 The question of security in quantum networks is just as critical 1170 as it is in the classical Internet, especially since enhanced 1171 security offered by quantum entanglement is one of the key 1172 driving factors. 1174 It turns out that as long as the underlying implementation 1175 corresponds to (or sufficiently approximates) theoretical models 1176 of quantum cryptography, quantum cryptographic protocols do not 1177 need the network to provide any guarantees about the 1178 confidentiality or integrity of the transmitted qubits or the 1179 generated entanglement. Instead, applications, such as QKD, 1180 establish such guarantees in an end-to-end fashion using the 1181 classical network in conjunction with the quantum one. 1183 Nevertheless, whilst applications can ensure their own secure 1184 operation, network protocols themselves should be security aware 1185 in order to protect the network itself and limit disruption. 1186 Whilst the applications remain secure they are not necessarily 1187 operational or as efficient in the presence of an attacker. 1188 Security concerns in quantum networks are described in more 1189 detail in [13] [12]. 1191 5. Make them easy to monitor 1193 In order to manage, evaluate the performance of, or debug a 1194 network it is necessary to have the ability to monitor the 1195 network. Quantum networks bring new challenges in this area so 1196 it should be a goal of a quantum network architecture to make 1197 this task easy. 1199 The fundamental unit of quantum information, the qubit, cannot be 1200 actively monitored as any readout irreversibly destroys its 1201 contents. One of the implications of this fact is that measuring 1202 an individual pair's fidelity is impossible. Fidelity is 1203 meaningful only as a statistical quantity which requires the 1204 constant monitoring and the sacrifice of generated Bell pairs for 1205 tomography or other methods. 1207 Furthermore, given one end of an entangled pair, it is impossible 1208 to tell where the other qubit is without any additional classical 1209 information. It is impossible to extract this information from 1210 the qubits themselves. This implies that tracking entangled 1211 pairs necessitates some exchange of classical information. 1213 6. Ensure availability and resilience 1215 Any practical and usable network, classical or quantum, must be 1216 able to continue to operate despite losses and failures, and be 1217 robust to malicious actors trying to disable connectivity. What 1218 differs in quantum networks as compared to classical networks in 1219 this regard is that we now have two data planes and two types of 1220 channels to worry about: a quantum and a classical one. 1221 Therefore, availability and resilience will most likely require a 1222 more advanced treatment than they do in classical networks. 1224 6.2. The principles of a quantum internet 1226 The principles support the goals, but are not goals themselves. The 1227 goals define what we want to build and the principles provide a 1228 guideline in how we might achieve this. The goals will also be the 1229 foundation for defining any metric of success for a network 1230 architecture, whereas the principles in themselves do not distinguish 1231 between success and failure. For more information about design 1232 considerations for quantum networks see [11] [14] . 1234 1. Entanglement is the fundamental service 1236 The key service that a quantum network provides is the 1237 distribution of entanglement between the nodes in a network. All 1238 distributed quantum applications are built on top of this key 1239 resource. Bell pairs are the minimal entanglement building block 1240 that is sufficient to develop these applications. However, a 1241 quantum network may also distribute multipartite entangled states 1242 (entangled states of three or more qubits)[20] as this may be 1243 more efficient under certain circumstances. 1245 2. Bell Pairs are indistinguishable 1247 Any two Bell Pairs between the same two nodes are 1248 indistinguishable for the purposes of an application provided 1249 they both satisfy its required fidelity threshold. This 1250 observation is likely to be key in enabling a more optimal 1251 allocation of resources in a network, e.g. for the purposes of 1252 provisioning resources to meet application demand. However, the 1253 qubits that make up the pair themselves are not indistinguishable 1254 and the two nodes operating on a pair must coordinate to make 1255 sure they are operating on qubits that belong to the same Bell 1256 Pair. 1258 3. Fidelity is part of the service 1260 In addition to being able to deliver Bell Pairs to the 1261 communication end-points, the Bell Pairs must be of sufficient 1262 fidelity. Unlike in classical networks where errors are 1263 effectively eliminated before reaching the application, many 1264 quantum applications only need imperfect entanglement to 1265 function. However, quantum applications will generally have a 1266 threshold for Bell pair fidelity below which they are no longer 1267 able to operate. Different applications will have different 1268 requirements for what fidelity they can work with. It is the 1269 network's responsibility to balance the resource usage with 1270 respect to the applications' requirements. It may be that it is 1271 cheaper for the network to provide lower fidelity pairs that are 1272 just above the threshold required by the application than it is 1273 to guarantee high fidelity pairs to all applications regardless 1274 of their requirements. 1276 4. Time is part of the service 1277 With the current technology, time is the most expensive resource. 1278 It is not the only resource that is in short supply (memory, and 1279 communication qubits are as well), but ultimately it is the 1280 lifetime of quantum memories that imposes the most difficult 1281 conditions for operating an extended network of quantum nodes. 1282 Current hardware has low rates of Bell Pair generation, short 1283 memory lifetimes, and access to a limited number of communication 1284 qubits. All these factors combined mean that even a short 1285 waiting queue at some node could be enough for the Bell Pairs to 1286 decohere. It is vital that quantum networks deliver entanglement 1287 in a timely manner. The meaning of timeliness will depend on the 1288 needs of the application (how long does it need to store the Bell 1289 pair in its own memory and/or what operations it wants to apply 1290 to it). 1292 5. Be flexible with regards to capabilities and limitations 1294 This goal encompasses two important points. First, the 1295 architecture should be able to function under the physical 1296 constraints imposed by the current generation hardware. Near- 1297 future hardware will have low entanglement generation rates, 1298 quantum memories able to hold a handful of qubits at best, and 1299 decoherence rates that will render many generated pairs unusable. 1301 Second, it should not make it difficult to run the network over 1302 any hardware that may come along in the future. The physical 1303 capabilities of repeaters will improve and redeploying a 1304 technology is extremely challenging. 1306 7. Comparison with classical networks 1308 Creating end-to-end Bell pairs between remote end-points is a 1309 stateful distributed task that requires a lot of a-priori 1310 coordination. Therefore, a connection-oriented approach seems the 1311 most natural for quantum networks. In this section, we discuss a 1312 plausible quantum network architecture inspired by MPLS. This is not 1313 an architecture proposal, but a thought experiment to give the reader 1314 an idea of what components are necessary for a functional quantum 1315 network. We use classical MPLS as a basis as it is well known and 1316 understood in the networking community. 1318 In connection-oriented quantum networks, when two quantum application 1319 end-points wish to start creating end-to-end Bell pairs, they must 1320 first create a quantum virtual circuit (QVC). As an analogy, in MPLS 1321 networks end-points must establish a label switched path (LSP) before 1322 exchanging traffic. Connection-oriented quantum networks may also 1323 support virtual circuits with multiple end-points for creating 1324 multipartite entanglement. As an analogy, MPLS networks have the 1325 concept of multi-point LSPs for multicast. 1327 When a quantum application creates a quantum virtual circuit, it can 1328 indicate quality of service (QoS) parameters such as the required 1329 capacity in end-to-end Bell pairs per second (BPPS) and the required 1330 fidelity of the Bell pairs. As an analogy, in MPLS networks 1331 applications specify the required bandwidth in bits per second (BPS) 1332 and other constraints when they create a new LSP. 1334 Quantum networks need a routing function to compute the optimal path 1335 (i.e. the best sequence of routers and links) for each new quantum 1336 virtual circuit. The routing function may be centralized or 1337 distributed. In the latter case, the quantum network needs a 1338 distributed routing protocol. As an analogy, classical networks use 1339 routing protocols such as open shortest path first (OSPF) and 1340 intermediate-system to intermediate system (IS-IS). 1342 Given the very scarce availability of resources in early quantum 1343 networks, a traffic engineering function is likely to be beneficial. 1344 Without traffic engineering, quantum virtual circuits always use the 1345 shortest path. In this case, the quantum network cannot guarantee 1346 that each quantum end-point will get its Bell pairs at the required 1347 rate or fidelity. This is analogous to "best effort" service in 1348 classical networks. 1350 With traffic engineering, quantum virtual circuits choose a path that 1351 is guaranteed to have the requested resources (e.g. bandwidth in 1352 BPPS) available, taking into account the capacity of the routers and 1353 links and taking into account the resources already consumed by other 1354 virtual circuits. As an analogy, both OSPF and IS-IS have traffic 1355 engineering (TE) extensions to keep track of used and available 1356 resources, and can use constrained shortest path first (CSPF) to take 1357 resource availability and other constraints into account when 1358 computing the optimal path. 1360 The use of traffic engineering implies the use of call admission 1361 control (CAC): the network denies any virtual circuits for which it 1362 cannot guarantee the requested quality of service a-priori. Or 1363 alternatively, the network pre-empts lower priority circuits to make 1364 room for the new one. 1366 Quantum networks need a signaling function: once the path for a 1367 quantum virtual circuit has been computed, signaling is used to 1368 install the "forwarding rules" into the data plane of each quantum 1369 router on the path. The signaling may be distributed, analogous to 1370 the resource reservation protocol (RSVP) in MPLS. Or the signaling 1371 may be centralized, similar to OpenFlow. 1373 Quantum networks need an abstraction of the hardware for specifying 1374 the forwarding rules. This allows us to de-couple the control plane 1375 (routing and signaling) from the data plane (actual creation of Bell 1376 pairs). The forwarding rules are specified using abstract building 1377 blocks such as "creating local Bell pairs", "swapping Bell pairs", 1378 "distillation of Bell pairs". As an analogy, classical networks use 1379 abstractions that are based on match conditions (e.g. looking up 1380 header fields in tables) and actions (e.g. modifying fields or 1381 forwarding a packet to a specific interface). The data-plane 1382 abstractions in quantum networks will be very different from those in 1383 classical networks due to the fundamental differences in technology 1384 and the stateful nature of quantum networks. In fact, choosing the 1385 right abstractions will be one of the biggest challenges when 1386 designing interoperable quantum network protocols. 1388 In quantum networks, control plane traffic (routing and signaling 1389 messages) is exchanged over a classical channel, whereas data plane 1390 traffic (the actual Bell pair qubits) is exchanged over a separate 1391 quantum channel. This is in contrast to most classical networks, 1392 where control plane traffic and data plane traffic share the same 1393 channel and where a single packet contains both user fields and 1394 header fields. There is, however, a classical analogy to the way 1395 quantum networks work. Generalized MPLS (GMPLS) networks use 1396 separate channels for control plane traffic and data plane traffic. 1397 Furthermore, GMPLS networks support data planes where there is no 1398 such thing as data plane headers (e.g. DWDM or TDM networks). 1400 8. Security Considerations 1402 Even though no user data enters a quantum network, security is listed 1403 as an explicit goal for the architecture and this issue is addressed 1404 in the section on goals. However, as this is an informational memo 1405 it does not propose any concrete mechanisms to achieve these goals. 1407 9. IANA Considerations 1409 This memo includes no request to IANA. 1411 10. Acknowledgements 1413 The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel 1414 Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang, 1415 Scott Fluhrer, and the rest of the QIRG community as a whole for 1416 their very useful reviews and comments to the document. 1418 11. Informative References 1420 [1] Carpenter, B., Ed., "Architectural Principles of the 1421 Internet", RFC 1958, DOI 10.17487/RFC1958, June 1996, 1422 . 1424 [2] Wang, C., Rahman, A., Li, R., and M. 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Rev. 1512 A Vol. 100, Iss. 5, 2019, 1513 . 1515 [21] Clark, D., "The design philosophy of the DARPA internet 1516 protocols", SIGCOMM '88, 1988, 1517 . 1519 Authors' Addresses 1521 Wojciech Kozlowski 1522 QuTech 1523 Building 22 1524 Lorentzweg 1 1525 Delft 2628 CJ 1526 Netherlands 1528 Email: w.kozlowski@tudelft.nl 1530 Stephanie Wehner 1531 QuTech 1532 Building 22 1533 Lorentzweg 1 1534 Delft 2628 CJ 1535 Netherlands 1537 Email: s.d.c.wehner@tudelft.nl 1539 Rodney Van Meter 1540 Keio University 1541 5322 Endo 1542 Fujisawa, Kanagawa 252-0882 1543 Japan 1545 Email: rdv@sfc.wide.ad.jp 1547 Bruno Rijsman 1548 Individual 1550 Email: brunorijsman@gmail.com 1551 Angela Sara Cacciapuoti 1552 University of Naples Federico II 1553 Department of Electrical Engineering and Information Technologies 1554 Claudio 21 1555 Naples 80125 1556 Italy 1558 Email: angelasara.cacciapuoti@unina.it 1560 Marcello Caleffi 1561 University of Naples Federico II 1562 Department of Electrical Engineering and Information Technologies 1563 Claudio 21 1564 Naples 80125 1565 Italy 1567 Email: marcello.caleffi@unina.it 1569 Shota Nagayama 1570 Mercari, Inc. 1571 Roppongi Hills Mori Tower 18F 1572 6-10-1 Roppongi, Minato-ku 1573 Tokyo 106-6118 1574 Japan 1576 Email: shota.nagayama@mercari.com