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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for intended status: Informational ---------------------------------------------------------------------------- == Outdated reference: A later version (-19) exists of draft-irtf-qirg-quantum-internet-use-cases-08 Summary: 0 errors (**), 0 flaws (~~), 2 warnings (==), 1 comment (--).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: 18 August 2022 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 14 February 2022 16 Architectural Principles for a Quantum Internet 17 draft-irtf-qirg-principles-10 19 Abstract 21 The vision of a quantum internet is to enhance existing 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 quantum entanglement 26 networks have been realised [Pompili21.1], but there is no practical 27 proposal for how to organise, utilise, and manage such networks. In 28 this draft, 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 18 August 2022. 51 Copyright Notice 53 Copyright (c) 2022 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 (https://trustee.ietf.org/ 58 license-info) in effect on the date of publication of this document. 59 Please review these documents carefully, as they describe your rights 60 and restrictions with respect to this document. Code Components 61 extracted from this document must include Revised BSD License text as 62 described in Section 4.e of the Trust Legal Provisions and are 63 provided without warranty as described in the Revised BSD License. 65 Table of Contents 67 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 68 2. Quantum information . . . . . . . . . . . . . . . . . . . . . 4 69 2.1. Quantum state . . . . . . . . . . . . . . . . . . . . . . 4 70 2.2. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 5 71 2.3. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 6 72 3. Entanglement as the fundamental resource . . . . . . . . . . 8 73 4. Achieving quantum connectivity . . . . . . . . . . . . . . . 9 74 4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 9 75 4.1.1. The measurement problem . . . . . . . . . . . . . . . 9 76 4.1.2. No-cloning theorem . . . . . . . . . . . . . . . . . 10 77 4.1.3. Fidelity . . . . . . . . . . . . . . . . . . . . . . 10 78 4.1.4. Inadequacy of direct transmission . . . . . . . . . . 11 79 4.2. Bell pairs . . . . . . . . . . . . . . . . . . . . . . . 11 80 4.3. Teleportation . . . . . . . . . . . . . . . . . . . . . . 12 81 4.4. The life cycle of entanglement . . . . . . . . . . . . . 13 82 4.4.1. Elementary link generation . . . . . . . . . . . . . 13 83 4.4.2. Entanglement swapping . . . . . . . . . . . . . . . . 14 84 4.4.3. Error Management . . . . . . . . . . . . . . . . . . 15 85 4.4.4. Delivery . . . . . . . . . . . . . . . . . . . . . . 19 86 5. Architecture of a quantum internet . . . . . . . . . . . . . 19 87 5.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 19 88 5.2. Classical communication . . . . . . . . . . . . . . . . . 21 89 5.3. Abstract model of the network . . . . . . . . . . . . . . 22 90 5.3.1. The control and data planes . . . . . . . . . . . . . 22 91 5.3.2. Elements of a quantum network . . . . . . . . . . . . 23 92 5.3.3. Putting it all together . . . . . . . . . . . . . . . 24 93 5.4. Physical constraints . . . . . . . . . . . . . . . . . . 25 94 5.4.1. Memory lifetimes . . . . . . . . . . . . . . . . . . 26 95 5.4.2. Rates . . . . . . . . . . . . . . . . . . . . . . . . 26 96 5.4.3. Communication qubits . . . . . . . . . . . . . . . . 26 97 5.4.4. Homogeneity . . . . . . . . . . . . . . . . . . . . . 27 98 6. Architectural principles . . . . . . . . . . . . . . . . . . 28 99 6.1. Goals of a quantum internet . . . . . . . . . . . . . . . 28 100 6.2. The principles of a quantum internet . . . . . . . . . . 32 101 7. A thought experiment inspired by classical networks . . . . . 34 102 8. Security Considerations . . . . . . . . . . . . . . . . . . . 36 103 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 36 104 10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 36 105 11. Informative References . . . . . . . . . . . . . . . . . . . 36 106 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 44 108 1. Introduction 110 Quantum networks are distributed systems of quantum devices that 111 utilise fundamental quantum mechanical phenomena such as 112 superposition, entanglement, and quantum measurement to achieve 113 capabilities beyond what is possible with non-quantum (classical) 114 networks [Kimble08]. Depending on the stage of a quantum network 115 [Wehner18] such devices may range from simple photonic devices 116 capable of preparing and measuring only one quantum bit (qubit) at a 117 time all the way to large-scale quantum computers of the future. A 118 quantum network is not meant to replace classical networks, but 119 rather form an overall hybrid classical-quantum network supporting 120 new capabilities which are otherwise impossible to realise 121 [VanMeterBook]. For example, the most well-known application of 122 quantum communication, quantum key distribution (QKD), can create and 123 distribute a pair of symmetric encryption keys in such a way that the 124 security of the entire process relies on the laws of physics (and 125 thus can be mathematically proven to be unbreakable) rather than the 126 intractability of certain mathematical problems [Bennett14] 127 [Ekert91]. Small networks capable of QKD have even already been 128 deployed at short (roughly 100km) distances [Elliott03] [Peev09] 129 [Aguado19] [Joshi20]. 131 The quantum networking paradigm also offers promise for a range of 132 new applications beyond quantum cryptography, such as distributed 133 quantum computation [Cirac99] [Crepeau02], secure quantum computing 134 in the cloud [Fitzsimons17], quantum-enhanced measurement networks 135 [Giovanetti04], or higher-precision, long-baseline telescopes 136 [Gottesman12]. These applications are much more demanding than QKD 137 and networks capable of executing them are in their infancy. The 138 first fully quantum, multinode network capable of sending, receiving, 139 and manipulating distributed quantum information has only recently 140 been realized [Pompili21.1] 142 Whilst a lot of effort has gone into physically realising and 143 connecting such devices, and making improvements to their speed and 144 error tolerance, there are no worked out proposals for how to run 145 these networks. To draw an analogy with a classical network, we are 146 at a stage where we can start to physically connect our devices and 147 send data, but all sending, receiving, buffer management, connection 148 synchronisation, and so on, must be managed by the application 149 directly by using low-level, custom-built, and hardware-specific 150 interfaces, rather than being managed by a network stack that exposes 151 a convenient high-level interface, such as sockets. Only recently, 152 was the first ever attempt at such a network stack experimentally 153 demonstrated in a laboratory setting [Pompili21.2]. Furthermore, 154 whilst physical mechanisms for transmitting quantum information 155 exist, there are no robust protocols for managing such transmissions. 157 This document, produced by the Quantum Internet Research Group 158 (QIRG), introduces quantum networks and presents general guidelines 159 for the design and construction of such networks. Overall, it is 160 intended as an introduction to the subject for network engineers and 161 researchers. It should not be considered as a conclusive statement 162 on how quantum network should or will be implemented. This document 163 was discussed on the QIRG mailing list and several IETF meetings and 164 represents the consensus of the QIRG members, both of experts in the 165 subject matter (from the quantum as well networking domain) as well 166 as newcomers who are the target audience. 168 2. Quantum information 170 In order to understand the framework for quantum networking, a basic 171 understanding of quantum information theory is necessary. The 172 following sections aim to introduce the minimum amount of knowledge 173 necessary to understand the principles of operation of a quantum 174 network. This exposition was written with a classical networking 175 audience in mind. It is assumed that the reader has never before 176 been exposed to any quantum physics. We refer the reader to 177 [SutorBook] and [NielsenChuang] for an in-depth introduction to 178 quantum information systems. 180 2.1. Quantum state 182 A quantum mechanical system is described by its quantum state. A 183 quantum state is an abstract object that provides a complete 184 description of the system at that particular moment. When combined 185 with the rules of the system's evolution in time, such as a quantum 186 circuit, it also then provides a complete description of the system 187 at all times. For the purposes of computing and networking, the 188 classical equivalent of a quantum state would be a string or stream 189 of logical bit values. These bits provide a complete description of 190 what values we can read out from that string at that particular 191 moment and when combined with its rules for evolution in time, such 192 as a logical circuit, we will also know its value at any other time. 194 Just like a single classical bit, a quantum mechanical system can be 195 simple and consist of a single particle, e.g. an atom or a photon of 196 light. In this case, the quantum state provides the complete 197 description of that one particle. Similarly, just like a string of 198 bits consists of multiple bits, a single quantum state can be used to 199 also describe an ensemble of many particles. However, because 200 quantum states are governed by the laws of quantum mechanics their 201 behaviour is significantly different to that of a string of bits. In 202 this section we will summarise the key concepts to understand these 203 differences and the we will explain their consequences for networking 204 in the rest of the draft. 206 2.2. Qubit 208 The differences between quantum computation and classical computation 209 begin at the bit-level. A classical computer operates on the binary 210 alphabet { 0, 1 }. A quantum bit, called a qubit, exists over the 211 same binary space, but unlike the classical bit, its state can exist 212 in a superposition of the two possibilities: 214 |qubit> = a |0> + b |1>, 216 where |X> is Dirac's ket notation for a quantum state (the value that 217 a qubit holds), here the binary 0 and 1, and the coefficients a and b 218 are complex numbers called probability amplitudes. Physically, such 219 a state can be realised using a variety of different technologies 220 such as electron spin, photon polarisation, atomic energy levels, and 221 so on. 223 Upon measurement, the qubit loses its superposition and irreversibly 224 collapses into one of the two basis states, either |0> or |1>. Which 225 of the two states it ends up in may not be deterministic, but can be 226 determined from the readout of the measurement. The measurement 227 result is a classical bit, 0 or 1, corresponding to |0> and |1> 228 respectively. The probability of measuring the state in the |0> 229 state is |a|^2 and similarly the probability of measuring the state 230 in the |1> state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness 231 is not due to our ignorance of the underlying mechanisms, but rather 232 is a fundamental feature of a quantum mechanical system [Aspect81]. 234 The superposition property plays an important role in fundamental 235 gate operations on qubits. Since a qubit can exist in a 236 superposition of its basis states, the elementary quantum gates are 237 able to act on all states of the superposition at the same time. For 238 example, consider the NOT gate: 240 NOT (a |0> + b |1>) -> a |1> + b |0>. 242 It is important to note that "qubit" can have two meanings. In the 243 first meaning, "qubit" refers to a physical quantum *system* whose 244 quantum state can be expressed as a superposition of two basis 245 states, which we often label |0> and |1>. Here, "qubit" refers to a 246 physical implementation akin to what a flip-flop, switch, voltage, or 247 current would be for a classical bit. In the second meaning, "qubit" 248 refers to the abstract quantum *state* of a quantum system with such 249 two basis states. In this case, the meaning of "qubit" is akin to 250 the logical value of a bit, from classical computing, i.e. "logical 251 0" or "logical 1". The two concepts are related, because a physical 252 "qubit" (first meaning) can be used to store the abstract "qubit" 253 (second meaning). Both meanings are used interchangeably in 254 literature and the meaning is generally clear from the context. 256 2.3. Multiple qubits 258 When multiple qubits are combined in a single quantum state the space 259 of possible states grows exponentially and all these states can 260 coexist in a superposition. For example, the general form of a two- 261 qubit register is 263 a |00> + b |01> + c |10> + d |11> 265 where the coefficients have the same probability amplitude 266 interpretation as for the single qubit state. Each state represents 267 a possible outcome of a measurement of the two-qubit register. For 268 example, |01> denotes a state in which the first qubit is in the 269 state |0> and the second is in the state |1>. 271 Performing single qubit gates affects the relevant qubit in each of 272 the superposition states. Similarly, two-qubit gates also act on all 273 the relevant superposition states, but their outcome is far more 274 interesting. 276 Consider a two-qubit register where the first qubit is in the 277 superposed state (|0> + |1>)/sqrt(2) and the other is in the 278 state |0>. This combined state can be written as: 280 (|0> + |1>)/sqrt(2) x |0> = (|00> + |10>)/sqrt(2), 282 where x denotes a tensor product (the mathematical mechanism for 283 combining quantum states together). 285 The constant 1/sqrt(2) is called the normalisation factor and 286 reflects the fact that the probabilities of measuring either a |0> or 287 a |1> for the first qubit add up to one. 289 Let us now consider the two-qubit controlled-NOT, or CNOT, gate. The 290 CNOT gate takes as input two qubits, a control and target, and 291 applies the NOT gate to the target if the control qubit is set. The 292 truth table looks like 294 +====+=====+ 295 | IN | OUT | 296 +====+=====+ 297 | 00 | 00 | 298 +----+-----+ 299 | 01 | 01 | 300 +----+-----+ 301 | 10 | 11 | 302 +----+-----+ 303 | 11 | 10 | 304 +----+-----+ 306 Table 1 308 Now, consider performing a CNOT gate on the state with the first 309 qubit being the control. We apply a two-qubit gate on all the 310 superposition states: 312 CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2). 314 What is so interesting about this two-qubit gate operation? The 315 final state is *entangled*. There is no possible way of representing 316 that quantum state as a product of two individual qubits; they are no 317 longer independent. That is, it is not possible to describe the 318 quantum state of either of the individual qubits in a way that is 319 independent of the other qubit. Only the quantum state of the system 320 that consists of both qubits provides a physically complete 321 description of the two-qubit system. The states of the two 322 individual qubits are now correlated beyond what is possible to 323 achieve classically. Neither qubit is in a definite |0> or |1> 324 state, but if we perform a measurement on either one, the outcome of 325 the partner qubit will *always* yield the exact same outcome. The 326 final state, whether it's |00> or |11>, is fundamentally random as 327 before, but the states of the two qubits following a measurement will 328 always be identical. One can think of this as flipping two coins, 329 but the coins always both land on "heads" or both land on "tails" 330 together. Something that we know is impossible classically. 332 Once a measurement is performed, the two qubits are once again 333 independent. The final state is either |00> or |11> and both of 334 these states can be trivially decomposed into a product of two 335 individual qubits. The entanglement has been consumed and the 336 entangled state must be prepared again. 338 3. Entanglement as the fundamental resource 340 Entanglement is the fundamental building block of quantum networks. 341 Consider the state from the previous section: 343 (|00> + |11>)/sqrt(2). 345 Neither of the two qubits is in a definite |0> or |1> state and we 346 need to know the state of the entire register to be able to fully 347 describe the behaviour of the two qubits. 349 Entangled qubits have interesting non-local properties. Consider 350 sending one of the qubits to another device. This device could in 351 principle be anywhere: on the other side of the room, in a different 352 country, or even on a different planet. Provided negligible noise 353 has been introduced, the two qubits will forever remain in the 354 entangled state until a measurement is performed. The physical 355 distance does not matter at all for entanglement. 357 This lies at the heart of quantum networking, because it is possible 358 to leverage the non-classical correlations provided by entanglement 359 in order to design completely new types of application protocols that 360 are not possible to achieve with just classical communication. 361 Examples of such applications are quantum cryptography [Bennett14] 362 [Ekert91], blind quantum computation [Fitzsimons17], or distributed 363 quantum computation [Crepeau02]. 365 Entanglement has two very special features from which one can derive 366 some intuition about the types of applications enabled by a quantum 367 network. 369 The first stems from the fact that entanglement enables stronger than 370 classical correlations, leading to opportunities for tasks that 371 require coordination. As a trivial example, consider the problem of 372 consensus between two nodes who want to agree on the value of a 373 single bit. They can use the quantum network to prepare the state 374 (|00> + |11>)/sqrt(2) with each node holding one of the two qubits. 375 Once either of the two nodes performs a measurement, the state of the 376 two qubits collapses to either |00> or |11>, so whilst the outcome is 377 random and does not exist before measurement, the two nodes will 378 always measure the same value. We can also build the more general 379 multi-qubit state (|00...> + |11...>)/sqrt(2) and perform the same 380 algorithm between an arbitrary number of nodes. These stronger than 381 classical correlations generalise to more complicated measurement 382 schemes as well. 384 The second feature of entanglement is that it cannot be shared, in 385 the sense that if two qubits are maximally entangled with each other, 386 then it is physically impossible for these two qubits to also be 387 entangled with a third qubit [Terhal04]. Hence, entanglement forms a 388 sort of private and inherently untappable connection between two 389 nodes once established. 391 Entanglement is created through local interactions between two qubits 392 or as a product of the way the qubits were created (e.g. entangled 393 photon pairs). To create a distributed entangled state, one can then 394 physically send one of the qubits to a remote node. It is also 395 possible to directly entangle qubits that are physically separated, 396 but this still requires local interactions between some other qubits 397 that the separated qubits are initially entangled with. Therefore, 398 it is the transmission of qubits that draws the line between a 399 genuine quantum network and a collection of quantum computers 400 connected over a classical network. 402 A quantum network is defined as a collection of nodes that is able to 403 exchange qubits and distribute entangled states amongst themselves. 404 A quantum node that is able only to communicate classically with 405 another quantum node is not a member of a quantum network. 407 More complex services and applications can be built on top of 408 entangled states distributed by the network, see e.g. [ZOO] 410 4. Achieving quantum connectivity 412 This section explains the meaning of quantum connectivity and the 413 necessary physical processes at an abstract level. 415 4.1. Challenges 417 A quantum network cannot be built by simply extrapolating all the 418 classical models to their quantum analogues. Sending qubits over a 419 wire like we send classical bits is simply not as easy to do. There 420 are several technological as well as fundamental challenges that make 421 classical approaches unsuitable in a quantum context. 423 4.1.1. The measurement problem 425 In classical computers and networks we can read out the bits stored 426 in memory at any time. This is helpful for a variety of purposes 427 such as copying, error detection and correction, and so on. This is 428 not possible with qubits. 430 A measurement of a qubit's state will destroy its superposition and 431 with it any entanglement it may have been part of. Once a qubit is 432 being processed, it cannot be read out until a suitable point in the 433 computation, determined by the protocol handling the qubit, has been 434 reached. Therefore, we cannot use the same methods known from 435 classical computing for the purposes of error detection and 436 correction. Nevertheless, quantum error detection and correction 437 schemes exist that take this problem into account and how a network 438 chooses to manage errors will have an impact on its architecture. 440 4.1.2. No-cloning theorem 442 Since directly reading the state of a qubit is not possible, one 443 could ask if we can simply copy a qubit without looking at it. 444 Unfortunately, this is fundamentally not possible in quantum 445 mechanics [Park70] [Wootters82]. 447 The no-cloning theorem states that it is impossible to create an 448 identical copy of an arbitrary, unknown quantum state. Therefore, it 449 is also impossible to use the same mechanisms that worked for 450 classical networks for signal amplification, retransmission, and so 451 on as they all rely on the ability to copy the underlying data. 452 Since any physical channel will always be lossy, connecting nodes 453 within a quantum network is a challenging endeavour and its 454 architecture must at its core address this very issue. 456 4.1.3. Fidelity 458 In general, it is expected that a classical packet arrives at its 459 destination without any errors introduced by hardware noise along the 460 way. This is verified at various levels through a variety of error 461 detection and correction mechanisms. Since we cannot read or copy a 462 quantum state, error detection and correction is more involved. 464 To describe the quality of a quantum state, a physical quantity 465 called fidelity is used [NielsenChuang]. Fidelity takes a value 466 between 0 and 1 -- higher is better, and less than 0.5 means the 467 state is unusable. It measures how close a quantum state is to the 468 state we have tried to create. It expresses the probability that the 469 state will behave exactly the same as our desired state. Fidelity is 470 an important property of a quantum system that allows us to quantify 471 how much a particular state has been affected by noise from various 472 sources (gate errors, channel losses, environment noise). 474 Interestingly, quantum applications do not need perfect fidelity to 475 be able to execute -- as long as the fidelity is above some 476 application-specific threshold, they will simply operate at lower 477 rates. Therefore, rather than trying to ensure that we always 478 deliver perfect states (a technologically challenging task) 479 applications will specify a minimum threshold for the fidelity and 480 the network will try its best to deliver it. A higher fidelity can 481 be achieved by either having hardware produce states of better 482 fidelity (sometimes one can sacrifice rate for higher fidelity) or by 483 employing quantum error detection and correction mechanisms (see 484 [Mural16] and [VanMeterBook] chapter 11). 486 4.1.4. Inadequacy of direct transmission 488 Conceptually, the most straightforward way to distribute an entangled 489 state is to simply transmit one of the qubits directly to the other 490 end across a series of nodes while performing sufficient forward 491 quantum error correction (Section 4.4.3.2) to bring losses down to an 492 acceptable level. Despite the no-cloning theorem and the inability 493 to directly measure a quantum state, error-correcting mechanisms for 494 quantum communication exist [Jiang09] [Fowler10] [Devitt13] 495 [Mural16]. However, quantum error correction makes very high demands 496 on both resources (physical qubits needed) and their initial 497 fidelity. Implementation is very challenging and quantum error 498 correction is not expected to be used until later generations of 499 quantum networks are possible (see [Mural16] figure 2 and 500 Section 4.4.3.3). Until then, quantum networks rely on entanglement 501 swapping (Section 4.4.2) and teleportation (Section 4.3). This 502 alternative relies on the observation that we do not need to be able 503 to distribute any arbitrary entangled quantum state. We only need to 504 be able to distribute any one of what are known as the Bell pair 505 states [Briegel98]. 507 4.2. Bell pairs 509 Bell pair states are the entangled two-qubit states: 511 |00> + |11>, |00> - |11>, |01> + |10>, |01> - |10>, 513 where the constant 1/sqrt(2) normalisation factor has been ignored 514 for clarity. Any of the four Bell pair states above will do, as it 515 is possible to transform any Bell pair into another Bell pair with 516 local operations performed on only one of the qubits. When each 517 qubit in a Bell pair is held by a separate node, either node can 518 apply a series of single qubit gates to their qubit alone in order to 519 transform the state between the different variants. 521 Distributing a Bell pair between two nodes is much easier than 522 transmitting an arbitrary quantum state over a network. Since the 523 state is known, handling errors becomes easier and small-scale error- 524 correction (such as entanglement distillation discussed in a later 525 section) combined with reattempts becomes a valid strategy. 527 The reason for using Bell pairs specifically as opposed to any other 528 two-qubit state is that they are the maximally entangled two-qubit 529 set of basis states. Maximal entanglement means that these states 530 have the strongest non-classical correlations of all possible two- 531 qubit states. Furthermore, since single-qubit local operations can 532 never increase entanglement, less entangled states would impose some 533 constraints on distributed quantum algorithms. This makes Bell pairs 534 particularly useful as a generic building block for distributed 535 quantum applications. 537 4.3. Teleportation 539 The observation that we only need to be able to distribute Bell pairs 540 relies on the fact that this enables the distribution of any other 541 arbitrary entangled state. This can be achieved via quantum state 542 teleportation [Bennett93]. Quantum state teleportation consumes an 543 unknown qubit state that we want to transmit and recreates it at the 544 desired destination. This does not violate the no-cloning theorem as 545 the original state is destroyed in the process. 547 To achieve this, an entangled pair needs to be distributed between 548 the source and destination before teleportation commences. The 549 source then entangles the transmission qubit with its end of the pair 550 and performs a read out of the two qubits (the sum of these 551 operations is called a Bell state measurement). This consumes the 552 Bell pair's entanglement, turning the source and destination qubits 553 into independent states. The measurements yields two classical bits 554 which the source sends to the destination over a classical channel. 555 Based on the value of the received two classical bits, the 556 destination performs one of four possible corrections (called the 557 Pauli corrections) on its end of the pair, which turns it into the 558 unknown qubit state that we wanted to transmit. This requirement to 559 communicate the measurement read out over a classical channel 560 unfortunately means that entanglement cannot be used to transmit 561 information faster than the speed of light. 563 The unknown quantum state that was transmitted was never fed into the 564 network itself. Therefore, the network needs to only be able to 565 reliably produce Bell pairs between any two nodes in the network. 566 Thus, a key difference between a classical and quantum data planes is 567 that a classical one carries user data, but a quantum data plane 568 provides the resources for the user to transmit user data themselves 569 without further involvement of the network. 571 4.4. The life cycle of entanglement 573 Reducing the problem of quantum connectivity to one of generating a 574 Bell pair has facilitated the problem, but it has not solved it. In 575 this section, we discuss how these entangled pairs are generated in 576 the first place, and how their two qubits are delivered to the end- 577 points. 579 4.4.1. Elementary link generation 581 In a quantum network, entanglement is always first generated locally 582 (at a node or an auxiliary element) followed by a movement of one or 583 both of the entangled qubits across the link through quantum 584 channels. In this context, photons (particles of light) are the 585 natural candidate for entanglement carriers, called flying qubits. 586 The rationale for this choice is related to the advantages provided 587 by photons such as moderate interaction with the environment leading 588 to moderate decoherence, convenient control with standard optical 589 components, and high-speed, low-loss transmissions. However, since 590 photons are hard to store, a transducer must transfer the flying 591 qubit's state to a qubit suitable for information processing and/or 592 storage (often referred to as a matter qubit). 594 Since this process may fail, in order to generate and store 595 entanglement efficiently, we must be able to distinguish successful 596 attempts from failures. Entanglement generation schemes that are 597 able to announce successful generation are called heralded 598 entanglement generation schemes. 600 There exist three basic schemes for heralded entanglement generation 601 on a link through coordinated action of the two nodes at the two ends 602 of the link [Cacciapuoti19]: 604 * "At mid-point": in this scheme an entangled photon pair source 605 sitting midway between the two nodes with matter qubits sends an 606 entangled photon through a quantum channel to each of the nodes. 607 There, transducers are invoked to transfer the entanglement from 608 the flying qubits to the matter qubits. In this scheme, the 609 transducers know if the transfers succeeded and are able to herald 610 successful entanglement generation via a message exchange over the 611 classical channel. 613 * "At source": in this scheme one of the two nodes sends a flying 614 qubit that is entangled with one of its matter qubits. A 615 transducer at the other end of the link will transfer the 616 entanglement from the flying qubit to one of its matter qubits. 617 Just like in the previous scheme, the transducer knows if its 618 transfer succeeded and is able to herald successful entanglement 619 generation with a classical message sent to the other node. 621 * "At both end-points": in this scheme both nodes send a flying 622 qubit that is entangled with one of their matter qubits. A 623 detector somewhere in between the nodes performs a joint 624 measurement on the two qubits, which stochastically projects the 625 remote matter qubits into an entangled quantum state. The 626 detector knows if the entanglement succeeded and is able to herald 627 successful entanglement generation by sending a message to each 628 node over the classical channel. 630 The "mid-point source" scheme is more robust to photon loss, but in 631 the other schemes the nodes retain greater control over the entangled 632 pair generation. 634 Note that whilst photons travel in a particular direction through the 635 quantum channel the resulting entangled pair of qubits does not have 636 a direction associated with it. Physically, there is no upstream or 637 downstream end of the pair. 639 4.4.2. Entanglement swapping 641 The problem with generating entangled pairs directly across a link is 642 that efficiency decreases with channel length. Beyond a few 10s of 643 kilometres in optical fibre or 1000 kilometres in free space (via 644 satellite) the rate is effectively zero and due to the no-cloning 645 theorem we cannot simply amplify the signal. The solution is 646 entanglement swapping [Briegel98]. 648 A Bell pair between any two nodes in the network can be constructed 649 by combining the pairs generated along each individual link on a path 650 between the two end-points. Each node along the path can consume the 651 two pairs on the two links that it is connected to in order to 652 produce a new entangled pair between the two remote ends. This 653 process is known as entanglement swapping. Pictorially it can be 654 represented as follows: 656 +---------+ +---------+ +---------+ 657 | A | | B | | C | 658 | |------| |------| | 659 | X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 | 660 +---------+ +---------+ +---------+ 661 where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2 662 are the qubits of entangled pair Y. The entanglement is denoted with 663 ~~. In the diagram above, nodes A and B share the pair X and nodes B 664 and C share the pair Y, but we want entanglement between A and C. 666 To achieve this goal, we simply teleport the qubit X2 using the pair 667 Y. This requires node B to perform a Bell state measurement on the 668 qubits X2 and Y1 which result in the destruction of the entanglement 669 between Y1 and Y2. However, X2 is recreated in Y2's place, carrying 670 with it its entanglement with X1. The end-result is shown below: 672 +---------+ +---------+ +---------+ 673 | A | | B | | C | 674 | |------| |------| | 675 | X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 | 676 +---------+ +---------+ +---------+ 678 Depending on the needs of the network and/or application, a final 679 Pauli correction at the recipient node may not be necessary since the 680 result of this operation is also a Bell pair. However, the two 681 classical bits that form the read out from the measurement at node B 682 must still be communicated, because they carry information about 683 which of the four Bell pairs was actually produced. If a correction 684 is not performed, the recipient must be informed which Bell pair was 685 received. 687 This process of teleporting Bell pairs using other entangled pairs is 688 called entanglement swapping. Quantum nodes that create long- 689 distance entangled pairs via entanglement swapping are called quantum 690 repeaters in academic literature [Briegel98] and we will use the same 691 terminology in this draft. 693 4.4.3. Error Management 695 4.4.3.1. Distillation 697 Neither the generation of Bell pairs nor the swapping operations are 698 noiseless operations. Therefore, with each link and each swap the 699 fidelity of the state degrades. However, it is possible to create 700 higher fidelity Bell pair states from two or more lower fidelity 701 pairs through a process called distillation (sometimes also referred 702 to as purification) [Dur07]. 704 To distil a quantum state, a second (and sometimes third) quantum 705 state is used as a "test tool" to test a proposition about the first 706 state, e.g., "the parity of the two qubits in the first state is 707 even." When the test succeeds, confidence in the state is improved, 708 and thus the fidelity is improved. The test tool states are 709 destroyed in the process, so resource demands increase substantially 710 when distillation is used. When the test fails, the tested state 711 must also be discarded. Distillation makes low demands on fidelity 712 and resources compared to quantum error correction, but distributed 713 protocols incur round-trip delays due to classical communication 714 [Bennett96]. 716 4.4.3.2. Quantum Error Correction 718 Just like classical error correction, quantum error correction (QEC) 719 encodes logical qubits using several physical (raw) qubits to protect 720 them from errors described in Section 4.1.3 [Jiang09] [Fowler10] 721 [Devitt13] [Mural16]. Furthermore, similarly to its classical 722 counterpart, QEC can not only correct state errors but also account 723 for lost qubits. Additionally, if all physical qubits which encode a 724 logical qubit are located at the same node, the correction procedure 725 can be executed locally, even if the logical qubit is entangled with 726 remote qubits. 728 Although QEC was originally a scheme proposed to protect a qubit from 729 noise, QEC can also be applied to entanglement distillation. Such 730 QEC-applied distillation is cost-effective but requires a higher base 731 fidelity. 733 4.4.3.3. Error management schemes 735 Quantum networks have been categorized into three "generations" based 736 on the error management scheme they employ [Mural16]. Note that 737 these "generations" are more like categories; they do not necessarily 738 imply a time progression and do not obsolete each other, though the 739 later generations do require more advanced technologies. Which 740 generation is used depends on the hardware platform and network 741 design choices. 743 Table 2 summarises the generations. 745 +===========+=================+=======================+============+ 746 | | First | Second generation | Third | 747 | | generation | | generation | 748 +===========+=================+=======================+============+ 749 | Loss | Heralded | Heralded entanglement | Quantum | 750 | tolerance | entanglement | generation (bi- | Error | 751 | | generation (bi- | directional classical | Correction | 752 | | directional | signaling) | (no | 753 | | classical | | classical | 754 | | signaling) | | signaling) | 755 +-----------+-----------------+-----------------------+------------+ 756 +-----------+-----------------+-----------------------+------------+ 757 | Error | Entanglement | Entanglement | Quantum | 758 | tolerance | distillation | distillation (uni- | Error | 759 | | (bi-directional | directional classical | Correction | 760 | | classical | signaling) or Quantum | (no | 761 | | signaling) | Error Correction (no | classical | 762 | | | classical signaling) | signaling) | 763 +-----------+-----------------+-----------------------+------------+ 765 Table 2: Classical signaling and generations 767 Generations are defined by the directions of classical signalling 768 required in their distributed protocols for loss tolerance and error 769 tolerance. Classical signalling carries the classical bits and 770 incurs round-trip delays described in Section 4.4.3.1, hence they 771 affect the performance of quantum networks, especially as the 772 distance between the communicating nodes increases. 774 Loss tolerance is about tolerating qubit transmission losses between 775 nodes. Heralded entanglement generation, as described in 776 Section 4.4.1, confirms the receipt of an entangled qubit using a 777 heralding signal. A pair of directly connected quantum nodes 778 repeatedly attempt to generate an entangled pair until the a 779 heralding signal is received. As described in Section 4.4.3.2, QEC 780 can be applied to complement lost qubits eliminating the need for re- 781 attempts. Furthermore, since the correction procedure is composed of 782 local operations, it does not require a heralding signal. However, 783 it is possible only when the photon loss rate from transmission to 784 measurement is less than 50%. 786 Error tolerance is about tolerating quantum state errors. 787 Entanglement distillation is the easiest mechanism for improved error 788 tolerance to implement, but it incurs round-trip delays due the 789 requirement for bi-directional classical signalling. The 790 alternative, QEC, is able to correct state errors locally so that it 791 does not need any classical signalling between the quantum nodes. In 792 between these two extremes, there is also QEC-applied distillation, 793 which requires uni-directional classical signalling. 795 The three "generations" summarised: 797 1. First generation quantum networks use heralding for loss 798 tolerance and entanglement distillation for error tolerance. 799 These networks can be implemented even with a limited set of 800 available quantum gates. 802 2. Second generation quantum networks improve upon the first 803 generation with QEC codes for error tolerance (but not loss 804 tolerance). At first, QEC will be applied to entanglement 805 distillation only which requires uni-directional classical 806 signalling. Later, QEC codes will be used to create logical Bell 807 pairs which no longer require any classical signalling for the 808 purposes of error tolerance. Heralding is still used to 809 compensate for transmission losses. 811 3. Third generation quantum networks directly transmit QEC encoded 812 qubits to adjacent nodes, as discussed in Section 4.1.4. 813 Elementary link Bell pairs can now be created without heralding 814 or any other classical signalling. Furthermore, this also 815 enables direct transmission architectures in which qubits are 816 forwarded end-to-end like classical packets rather than relying 817 on Bell pairs and entanglement swapping. 819 Despite the fact that there are important distinctions in how errors 820 will be managed in the different generations it is unlikely that all 821 quantum networks will consistently use the same method. This is due 822 to different hardware requirements of the different generations and 823 the practical reality of network upgrades. Therefore, it is 824 unavoidable that eventually boundaries between different error 825 management schemes start forming. This will affect the content and 826 semantics of messages that must cross those boundaries -- both for 827 connection setup and real-time operation [Nagayama16]. 829 4.4.4. Delivery 831 Eventually, the Bell pairs must be delivered to an application (or 832 higher layer protocol) at the two end-nodes. A detailed list of such 833 requirements is beyond the scope of this draft. At minimum, the end- 834 nodes require information to map a particular Bell pair to the qubit 835 in their local memory that is part of this entangled pair. 837 5. Architecture of a quantum internet 839 It is evident from the previous sections that the fundamental service 840 provided by a quantum network significantly differs from that of a 841 classical network. Therefore, it is not surprising that the 842 architecture of a quantum internet will itself be very different from 843 that of the classical Internet. 845 5.1. Challenges 847 This subsection covers the major fundamental challenges building 848 quantum networks. Here, we only describe the fundamental 849 differences. Technological limitations are described later. 851 1. Bell pairs are not equivalent to payload carrying packets. 853 In most classical networks, including Ethernet, Internet Protocol 854 (IP), and Multi-Protocol Label Switching (MPLS) networks, user 855 data is grouped into packets. In addition to the user data, each 856 packet also contains a series of headers which contain the 857 control information that lets routers and switches forward it 858 towards its destination. Packets are the fundamental unit in a 859 classical network. 861 In a quantum network, the entangled pairs of qubits are the basic 862 unit of networking. These qubits themselves do not carry any 863 headers. Therefore, quantum networks will have to send all 864 control information via separate classical channels which the 865 repeaters will have to correlate with the qubits stored in their 866 memory. Furthermore, a Bell pair consists of two qubits 867 distributed across two nodes which is unlike a classical packet 868 which is located at a single node. This has a fundamental impact 869 on how quantum networks will be managed and how protocols need to 870 be designed. To make long-distance Bell pairs, the nodes may 871 have to keep their qubits in their quantum memories and wait 872 until control information is exchanged before proceeding with the 873 next operation. This signalling will result in additional 874 latency which will depend on the distance between the nodes 875 holding the two ends of the Bell pair. Error management, such as 876 entanglement distillation, is a typical example of such control 877 information exchange [Nagayama21] (see also Section 4.4.3.3). 879 2. "Store and forward" vs "store and swap" quantum networks. 881 As described in Section 4.4.1, quantum links provide Bell pairs 882 that are undirected network resources, in contrast to directed 883 frames of classical networks. This phenomenological distinction 884 leads to architectural differences between quantum networks and 885 classical networks. Quantum networks combine multiple elementary 886 link Bell pairs together to create one end-to-end Bell pair, 887 whereas classical networks deliver messages from one end to the 888 other end hop by hop. 890 Classical networks receive data on one interface, store it in 891 local buffers, then forward the data to another appropriate 892 interface. Quantum networks store Bell pairs and then execute 893 entanglement swapping instead of forwarding in the data plane. 894 Such quantum networks are "store and swap" networks. In "store 895 and swap" networks, we do not need to care about the order in 896 which the Bell pairs were generated since they are undirected. 897 However, whilst the ordering does not matter, it is very 898 important that the right entangled pairs get swapped, and that 899 the intermediate measurement outcomes (see Section 4.4.2) are 900 signalled to and correlated with the correct qubits at the other 901 nodes. Otherwise, the final end-to-end entangled pair will not 902 be created between the expected end-points or will be in a 903 different quantum state than expected. For example, rather than 904 Alice receiving a qubit that is entangled with Bob's qubit, her 905 qubit is entangled with Charlie's qubit. This distinction makes 906 control algorithms and optimisation of quantum networks different 907 from classical ones, in the sense that swapping is stateful in 908 contrast to stateless packet-by-packet forwarding. Note that 909 third generation quantum networks, as described in Section 4.4.1, 910 will be able to support a "store and forward" architecture in 911 addition to "store and swap". 913 3. An entangled pair is only useful if the locations of both qubits 914 are known. 916 A classical network packet logically exists only at one location 917 at any point in time. If a packet is modified in some way, 918 whether headers or payload, this information does not need to be 919 conveyed to anybody else in the network. The packet can be 920 simply forwarded as before. 922 In contrast, entanglement is a phenomenon in which two or more 923 qubits exist in a physically distributed state. Operations on 924 one of the qubits change the mutual state of the pair. Since the 925 owner of a particular qubit cannot just read out its state, it 926 must coordinate all its actions with the owner of the pair's 927 other qubit. Therefore, the owner of any qubit that is part of 928 an entangled pair must know the location of its counterpart. 929 Location, in this context, need not be the explicit spatial 930 location. A relevant pair identifier, a means of communication 931 between the pair owners, and an association between the pair ID 932 and the individual qubits is sufficient. 934 4. Generating entanglement requires temporary state. 936 Packet forwarding in a classical network is largely a stateless 937 operation. When a packet is received, the router does a lookup 938 in its forwarding table and sends the packet out of the 939 appropriate output. There is no need to keep any memory of the 940 packet any more. 942 A quantum node must be able to make decisions about qubits that 943 it receives and is holding in its memory. Since qubits do not 944 carry headers, the receipt of an entangled pair conveys no 945 control information based on which the repeater can make a 946 decision. The relevant control information will arrive 947 separately over a classical channel. This implies that a 948 repeater must store temporary state as the control information 949 and the qubit it pertains to will, in general, not arrive at the 950 same time. 952 5.2. Classical communication 954 In this draft we have already covered two different roles that 955 classical communication must perform: 957 * communicate classical bits of information as part of distributed 958 protocols such as entanglement swapping and teleportation, 960 * communicate control information within a network, including both 961 background protocols such as routing as well as signalling 962 protocols to set up end-to-end entanglement generation. 964 Classical communication is a crucial building block of any quantum 965 network. All nodes in a quantum network are assumed to have 966 classical connectivity with each other (within typical administrative 967 domain limits). Therefore, quantum nodes will need to manage two 968 data planes in parallel, a classical one and a quantum one. 969 Additionally, a node must be able to correlate information between 970 the two planes so that the control information received on a 971 classical channel can be applied to the qubits managed by the quantum 972 data plane. 974 5.3. Abstract model of the network 976 5.3.1. The control and data planes 978 Control plane protocols for quantum networks will have many 979 responsibilities similar to their classical counterparts, namely 980 discovering the network topology, resource management, populating 981 data plane tables, etc. Most of these protocols do not require the 982 manipulation of quantum data and can operate simply by exchanging 983 classical messages only. There may also be some control plane 984 functionality that does require the handling of quantum data, e.g. a 985 quantum ping [I-D.irtf-qirg-quantum-internet-use-cases]. As it is 986 not clear if there is much benefit in defining a separate quantum 987 control plane given the significant overlap in responsibilities with 988 its classical counterpart, the question of whether there should be a 989 separate quantum control plane is beyond the scope of this document. 991 However, the data plane separation is much more distinct and there 992 will be two data planes: a classical data plane and a quantum data 993 plane. The classical data plane processes and forwards classical 994 packets. The quantum data plane processes and swaps entangled pairs. 995 Third generation quantum networks may also forward qubits in addition 996 to swapping Bell pairs. 998 In addition to control plane messages, there will also be control 999 information messages that operate at the granularity of individual 1000 entangled pairs, such as heralding messages used for elementary link 1001 generation (Section 4.4.1). In terms of functionality, these 1002 messages are closer to classical packet headers than control plane 1003 messages and thus we consider them to be part of the quantum data 1004 plane. Therefore, a quantum data plane also includes the exchange of 1005 classical control information at the granularity of individual qubits 1006 and entangled pairs. 1008 5.3.2. Elements of a quantum network 1010 We have identified quantum repeaters as the core building block of a 1011 quantum network. However, a quantum repeater will have to do more 1012 than just entanglement swapping in a functional quantum network. Its 1013 key responsibilities will include: 1015 1. Creating link-local entanglement between neighbouring nodes. 1017 2. Extending entanglement from link-local pairs to long-range pairs 1018 through entanglement swapping. 1020 3. Performing distillation to manage the fidelity of the produced 1021 pairs. 1023 4. Participating in the management of the network (routing, etc.). 1025 Not all quantum repeaters in the network will be the same; here we 1026 break them down further: 1028 * Quantum routers (controllable quantum nodes) - A quantum router is 1029 a quantum repeater with a control plane that participates in the 1030 management of the network and will make decisions about which 1031 qubits to swap to generate the requested end-to-end pairs. 1033 * Automated quantum nodes - An automated quantum node is a data 1034 plane only quantum repeater that does not participate in the 1035 network control plane. Since the no-cloning theorem precludes the 1036 use of amplification, long-range links will be established by 1037 chaining multiple such automated nodes together. 1039 * End-nodes - End-nodes in a quantum network must be able to receive 1040 and handle an entangled pair, but they do not need to be able to 1041 perform an entanglement swap (and thus are not necessarily quantum 1042 repeaters). End-nodes are also not required to have any quantum 1043 memory as certain quantum applications can be realised by having 1044 the end-node measure its qubit as soon as it is received. 1046 * Non-quantum nodes - Not all nodes in a quantum network need to 1047 have a quantum data plane. A non-quantum node is any device that 1048 can handle classical network traffic. 1050 Additionally, we need to identify two kinds of links that will be 1051 used in a quantum network: 1053 * Quantum links - A quantum link is a link which can be used to 1054 generate an entangled pair between two directly connected quantum 1055 repeaters. This may include additional mid-point elements 1056 described in Section 4.4.1. It may also include a dedicated 1057 classical channel that is to be used solely for the purpose of 1058 coordinating the entanglement generation on this quantum link. 1060 * Classical links - A classical link is a link between any node in 1061 the network that is capable of carrying classical network traffic. 1063 Note that passive elements, such as optical switches, do not destroy 1064 the quantum state. Therefore, it is possible to connect multiple 1065 quantum nodes with each other over an optical network and perform 1066 optical switching rather than routing via entanglement swapping at 1067 quantum routers. This does require coordination with the elementary 1068 link entanglement generation process and it still requires repeaters 1069 to overcome the short-distance limitations. However, this is a 1070 potentially feasible architecture for local area networks. 1072 5.3.3. Putting it all together 1074 A two-hop path in a generic quantum network can be represented as: 1076 +-----+ +-----+ 1077 | App |- - - - - - - - - -CC- - - - - - - - - -| App | 1078 +-----+ +------+ +-----+ 1079 | EN |------ CL ------| QR |------ CL ------| EN | 1080 | |------ QL ------| |------ QL ------| | 1081 +-----+ +------+ +-----+ 1083 App - user-level application 1084 EN - end-node 1085 QL - quantum link 1086 CL - classical link 1087 CC - classical channel (traverses one or more CLs) 1088 QR - quantum repeater 1090 An application (App) running on two end-nodes (ENs) attached to a 1091 network will at some point need the network to generate entangled 1092 pairs for its use. This may require negotiation between the end- 1093 nodes (possibly ahead of time), because they must both open a 1094 communication end-point which the network can use to identify the two 1095 ends of the connection. The two end-nodes use a classical channel 1096 (CC) available in the network to achieve this goal. 1098 When the network receives a request to generate end-to-end entangled 1099 pairs it uses the classical communication links (CLs) to coordinate 1100 and claim the resources necessary to fulfill this request. This may 1101 be some combination of prior control information (e.g. routing 1102 tables) and signalling protocols, but the details of how this is 1103 achieved are an active research question. A thought experiment on 1104 what this might look like be can be found later in this draft in 1105 Section 7 1107 During or after the distribution of control information, the network 1108 performs the necessary quantum operations such as generating 1109 entanglement over individual quantum links (QLs), performing 1110 entanglement swaps at quantum repeaters (QRs), and further signalling 1111 to transmit the swap outcomes and other control information. Since 1112 Bell pairs do not carry any user data, some of these operations can 1113 be performed before the request is received in anticipation of the 1114 demand. 1116 The entangled pair is delivered to the application once it is ready, 1117 together with the relevant pair identifier. However, being ready 1118 does not necessarily mean that all link pairs and entanglement swaps 1119 are complete, as some applications can start executing on an 1120 incomplete pair. In this case the remaining entanglement swaps will 1121 propagate the actions across the network to the other end, sometimes 1122 necessitating fixup operations at the end node. 1124 5.4. Physical constraints 1126 The model above has effectively abstracted away the particulars of 1127 the hardware implementation. However, certain physical constraints 1128 need to be considered in order to build a practical network. Some of 1129 these are fundamental constraints and no matter how much the 1130 technology improves, they will always need to be addressed. Others 1131 are artifacts of the early stages of a new technology. Here, we 1132 consider a highly abstract scenario and refer to [Wehner18] for 1133 pointers to the physics literature. 1135 5.4.1. Memory lifetimes 1137 In addition to discrete operations being imperfect, storing a qubit 1138 in memory is also highly non-trivial. The main difficulty in 1139 achieving persistent storage is that it is extremely challenging to 1140 isolate a quantum system from the environment. The environment 1141 introduces an uncontrollable source of noise into the system which 1142 affects the fidelity of the state. This process is known as 1143 decoherence. Eventually, the state has to be discarded once its 1144 fidelity degrades too much. 1146 The memory lifetime depends on the particular physical setup, but the 1147 highest achievable values in quantum network hardware currently are 1148 on the order of seconds [Abobeih18] although a lifetime of a minute 1149 has also been demonstrated for qubits not connected to a quantum 1150 network [Bradley19] (as of 2020). These values have increased 1151 tremendously over the lifetime of the different technologies and are 1152 bound to keep increasing. However, if quantum networks are to be 1153 realised in the near future, they need to be able to handle short 1154 memory lifetimes, for example by reducing latency on critical paths. 1156 5.4.2. Rates 1158 Entanglement generation on a link between two connected nodes is not 1159 a very efficient process and it requires many attempts to succeed 1160 [Hensen15] [Dahlberg19]. For example, the highest achievable rates 1161 of success between nitrogen-vacancy center nodes, which in addition 1162 to entanglement generation are also capable of storing and processing 1163 the resulting qubits, are on the order of 10 Hz. Combined with short 1164 memory lifetimes this leads to very tight timing windows to build up 1165 network-wide connectivity. 1167 Other platforms have shown higher entanglement rates, but this 1168 usually comes at the cost of other hardware capabilities, such as no 1169 quantum memory and/or limited processing capabilities [Wei22]. 1170 Nevertheless, the current rates are not sufficient for practical 1171 applications beyond simple experimental proofs of concept. However, 1172 they are expected to improve over time as quantum network technology 1173 evolves [Wei22]. 1175 5.4.3. Communication qubits 1177 Most physical architectures capable of storing qubits are only able 1178 to generate entanglement using only a subset of available qubits 1179 called communication qubits [Dahlberg19]. Once a Bell pair has been 1180 generated using a communication qubit, its state can be transferred 1181 into memory. This may impose additional limitations on the network. 1182 In particular, if a given node has only one communication qubit it 1183 cannot simultaneously generate Bell pairs over two links. It must 1184 generate entanglement over the links one at a time. 1186 5.4.4. Homogeneity 1188 Currently all existing quantum network implementations are 1189 homogeneous and they do not interface with each other. In general, 1190 it is very challenging to combine different quantum information 1191 processing technologies. 1193 There are many different physical hardware platforms for implementing 1194 quantum networking hardware. The different technologies differ in 1195 how they store and manipulate qubits in memory and how they generate 1196 entanglement across a link with their neighbours. For example, 1197 hardware based on optical elements and atomic ensembles [Sangouard11] 1198 is very efficient at generating entanglement at high rates, but 1199 provides limited processing capabilities once the entanglement is 1200 generated. On the other hand, nitrogen-vacancy based [Hensen15] or 1201 trapped ion [Moehring07] platforms offer a much greater degree of 1202 control over the qubits, but have a harder time generating 1203 entanglement at high rates. 1205 In order to overcome the weaknesses of the different platforms, 1206 coupling the different technologies will help to build fully 1207 functional networks. For example, end-nodes may be implemented using 1208 technology with good qubit processing capabilities to enable complex 1209 applications, but automated quantum nodes that that serve only to 1210 "repeat" along a linear chain, where the processing logic is much 1211 simpler, can be implemented with technologies that sacrifice 1212 processing capabilities for higher entanglement rates at long 1213 distances [Askarani21]. 1215 This point is further exacerbated by the fact that quantum computers 1216 (i.e. end-nodes in a quantum network) are often based on different 1217 hardware platforms than quantum repeaters thus requiring a coupling 1218 (transduction) between the two. This is especially true for quantum 1219 computers based on superconducting technology which are challenging 1220 to connect to optical networks. However, even trapped ion quantum 1221 computers, which is a platform that has shown promise for quantum 1222 networking, will still need to connect to other platforms that are 1223 better at creating entanglement at high rates over long distances 1224 (hundreds of kms). 1226 6. Architectural principles 1228 Given that the most practical way of realising quantum network 1229 connectivity is using Bell pair and entanglement swapping repeater 1230 technology, what sort of principles should guide us in assembling 1231 such networks such that they are functional, robust, efficient, and 1232 most importantly, do they work? Furthermore, how do we design 1233 networks so that they work under the constraints imposed by the 1234 hardware available today, but do not impose unnecessary burdens on 1235 future technology? 1237 As quantum networking is a completely new technology that is likely 1238 to see many iterations over its lifetime, this draft must not serve 1239 as a definitive set of rules, but merely as a general set of 1240 recommended guidelines for the first generations of quantum networks 1241 based on principles and observations made by the community. The 1242 benefit of having a community built document at this early stage is 1243 that expertise in both quantum information and network architecture 1244 is needed in order to successfully build a quantum internet. 1246 6.1. Goals of a quantum internet 1248 When outlining any set of principles we must ask ourselves what goals 1249 do we want to achieve as inevitably trade-offs must be made. So what 1250 sort of goals should drive a quantum network architecture? The 1251 following list has been inspired by the history of computer 1252 networking and thus it is inevitably very similar to one that could 1253 be produced for the classical Internet [Clark88]. However, whilst 1254 the goals may be similar the challenges involved are often 1255 fundamentally different. The list will also most likely evolve with 1256 time and the needs of its users. 1258 1. Support distributed quantum applications 1260 This goal seems trivially obvious, but makes a subtle, but 1261 important point which highlights a key difference between quantum 1262 and classical networks. Ultimately, quantum data transmission is 1263 not the goal of a quantum network - it is only one possible 1264 component of more advanced quantum application protocols 1265 [Wehner18]. Whilst transmission certainly could be used as a 1266 building block for all quantum applications, it is not the most 1267 basic one possible. For example, entanglement-based QKD, the 1268 most well known quantum application protocol, only relies on the 1269 stronger-than-classical correlations and inherent secrecy of 1270 entangled Bell pairs and does not have to transmit arbitrary 1271 quantum states [Ekert91]. 1273 The primary purpose of a quantum internet is to support 1274 distributed quantum application protocols and it is of utmost 1275 importance that they can run well and efficiently. Thus, it is 1276 important to develop performance metrics meaningful to 1277 application to drive the development of quantum network 1278 protocols. For example, the Bell pair generation rate is 1279 meaningless if one does not also consider their fidelity. It is 1280 generally much easier to generate pairs of lower fidelity, but 1281 quantum applications may have to make multiple re-attempts or 1282 even abort if the fidelity is too low. A review of the 1283 requirements for different known quantum applications can be 1284 found in [Wehner18] and an overview of use-cases can be found in 1285 [I-D.irtf-qirg-quantum-internet-use-cases]. 1287 2. Support tomorrow's distributed quantum applications 1289 The only principle of the Internet that should survive 1290 indefinitely is the principle of constant change [RFC1958]. 1291 Technical change is continuous and the size and capabilities of 1292 the quantum internet will change by orders of magnitude. 1293 Therefore, it is an explicit goal that a quantum internet 1294 architecture be able to embrace this change. We have the benefit 1295 of having been witness to the evolution of the classical Internet 1296 over several decades and seen what worked and what did not. It 1297 is vital for a quantum internet to avoid the need for flag days 1298 (e.g. NCP to TCP/IP) or upgrades that take decades to roll out 1299 (e.g. IPv4 to IPv6). 1301 Therefore, it is important that any proposed architecture for 1302 general purpose quantum repeater networks can integrate new 1303 devices and solutions as they become available. The architecture 1304 should not be constrained due to considerations for early-stage 1305 hardware and applications. For example, it is already possible 1306 to run QKD efficiently on metropolitan scales and such networks 1307 are already commercially available. However, they are not based 1308 on quantum repeaters and thus will not be able to easily 1309 transition to more sophisticated applications. 1311 3. Support heterogeneity 1313 There are multiple proposals for realising practical quantum 1314 repeater hardware and they all have their advantages and 1315 disadvantages. Some may offer higher Bell pair generation rates 1316 on individual links at the cost of more difficult entanglement 1317 swap operations. Other platforms may be good all around, but are 1318 more difficult to build. 1320 In addition to physical boundaries, there may be distinctions in 1321 how errors are managed (Section 4.4.3.3). These difference will 1322 affect the content and semantics of messages that cross these 1323 boundaries -- both for connection setup and real-time operation. 1325 The optimal network configuration will likely leverage the 1326 advantages of multiple platforms to optimise the provided 1327 service. Therefore, it is an explicit goal to incorporate varied 1328 hardware and technology support from the beginning. 1330 4. Ensure security at the network level 1332 The question of security in quantum networks is just as critical 1333 as it is in the classical Internet, especially since enhanced 1334 security offered by quantum entanglement is one of the key 1335 driving factors. 1337 Fortunately, from an application's point of view, as long as the 1338 underlying implementation corresponds to (or sufficiently 1339 approximates) theoretical models of quantum cryptography, quantum 1340 cryptographic protocols do not need the network to provide any 1341 guarantees about the confidentiality or integrity of the 1342 transmitted qubits or the generated entanglement (though they may 1343 impose requirements on the classical channel, e.g to be 1344 authenticated [Wang21]). Instead, applications will leverage the 1345 classical networks to establish the end-to-end security of the 1346 results obtained from the processing of entangled qubits. 1347 However, it is important to note that whilst classical networks 1348 are necessary to establish these end-to-end guarantees, the 1349 security relies on the properties of quantum entanglement. For 1350 example, QKD uses classical information reconciliation [Tang19] 1351 for error correction and privacy amplification [Elkouss11] for 1352 generating the final secure key, but the raw bits that are fed 1353 into these protocols must come from measuring entangled qubits 1354 [Ekert91]. In another application, secure delegated quantum 1355 computing, the client hides its computation from the server by 1356 sending qubits to the server and then requesting it (in a 1357 classical message) to measure them in an encoded basis. The 1358 client then decodes the results it receives from the server to 1359 obtain the result of the computation [Broadbent10]. Once again, 1360 whilst a classical network is used to achieve the goal of secure 1361 computation, the remote computation is strictly quantum. 1363 Nevertheless, whilst applications can ensure their own end-to-end 1364 security, network protocols themselves should be security aware 1365 in order to protect the network itself and limit disruption. 1366 Whilst the applications remain secure they are not necessarily 1367 operational or as efficient in the presence of an attacker. For 1368 example, if an attacker can measure every qubit between two 1369 parties trying to establish a key using QKD, no secret key can be 1370 generated. Security concerns in quantum networks are described 1371 in more detail in [Satoh17] [Satoh20]. 1373 5. Make them easy to monitor 1375 In order to manage, evaluate the performance of, or debug a 1376 network it is necessary to have the ability to monitor the 1377 network while ensuring there will be mechanisms in place to 1378 protect the confidentiality and integrity of the devices 1379 connected to it. Quantum networks bring new challenges in this 1380 area so it should be a goal of a quantum network architecture to 1381 make this task easy. 1383 The fundamental unit of quantum information, the qubit, cannot be 1384 actively monitored as any readout irreversibly destroys its 1385 contents. One of the implications of this fact is that measuring 1386 an individual pair's fidelity is impossible. Fidelity is 1387 meaningful only as a statistical quantity which requires the 1388 constant monitoring and the sacrifice of generated Bell pairs for 1389 tomography or other methods. 1391 Furthermore, given one end of an entangled pair, it is impossible 1392 to tell where the other qubit is without any additional classical 1393 metadata. It is impossible to extract this information from the 1394 qubits themselves. This implies that tracking entangled pairs 1395 necessitates some exchange of classical information. This 1396 information might include (i) a reference to the entangled pair 1397 that allows distributed applications to coordinate actions on 1398 qubits of the same pair, and (ii) the two bits from each 1399 entanglement swap necessary to identify the final state of the 1400 Bell pair (Section 4.4.2). 1402 6. Ensure availability and resilience 1404 Any practical and usable network, classical or quantum, must be 1405 able to continue to operate despite losses and failures, and be 1406 robust to malicious actors trying to disable connectivity. What 1407 differs in quantum networks as compared to classical networks in 1408 this regard is that we now have two data planes and two types of 1409 channels to worry about: a quantum and a classical one. 1410 Therefore, availability and resilience will most likely require a 1411 more advanced treatment than they do in classical networks. 1413 6.2. The principles of a quantum internet 1415 The principles support the goals, but are not goals themselves. The 1416 goals define what we want to build and the principles provide a 1417 guideline in how we might achieve this. The goals will also be the 1418 foundation for defining any metric of success for a network 1419 architecture, whereas the principles in themselves do not distinguish 1420 between success and failure. For more information about design 1421 considerations for quantum networks see [VanMeter13.1] [Dahlberg19]. 1423 1. Entanglement is the fundamental service 1425 The key service that a quantum network provides is the 1426 distribution of entanglement between the nodes in a network. All 1427 distributed quantum applications are built on top of this key 1428 resource. Applications such as clustered quantum computing, 1429 distributed quantum computing, distributed quantum sensing 1430 networks, and certain kinds of quantum secure networks all 1431 consume quantum entanglement as a resource. Some applications 1432 (e.g. quantum key distribution) simply measure the entangled 1433 qubits to obtain a shared secret key [QKD]. Other applications 1434 (e.g. distributed quantum computing) build more complex 1435 abstractions and operations on the entangled qubits, e.g., 1436 distributed CNOT gates [DistCNOT] or teleportation of arbitrary 1437 qubit states [Teleportation]. 1439 A quantum network may also distribute multipartite entangled 1440 states (entangled states of three or more qubits) [Meignant19] 1441 which are useful for applications such as conference key 1442 agreement [Murta20], distributed quantum computing [Cirac99], 1443 secret sharing [Qin17], and clock synchronisation [Komar14]. 1444 Though it was worth noting that multipartite entangled states can 1445 also be constructed from multiple entangled pairs distributed 1446 between the end-nodes. 1448 2. Bell Pairs are indistinguishable 1450 Any two Bell Pairs between the same two nodes are 1451 indistinguishable for the purposes of an application provided 1452 they both satisfy its required fidelity threshold. This 1453 observation is likely to be key in enabling a more optimal 1454 allocation of resources in a network, e.g. for the purposes of 1455 provisioning resources to meet application demand. However, the 1456 qubits that make up the pair themselves are not indistinguishable 1457 and the two nodes operating on a pair must coordinate to make 1458 sure they are operating on qubits that belong to the same Bell 1459 pair. 1461 3. Fidelity is part of the service 1463 In addition to being able to deliver Bell pairs to the 1464 communication end-points, the Bell Pairs must be of sufficient 1465 fidelity. Unlike in classical networks where most errors are 1466 effectively eliminated before reaching the application, many 1467 quantum applications only need imperfect entanglement to 1468 function. However, quantum applications will generally have a 1469 threshold for Bell pair fidelity below which they are no longer 1470 able to operate. Different applications will have different 1471 requirements for what fidelity they can work with. It is the 1472 network's responsibility to balance the resource usage with 1473 respect to the applications' requirements. It may be that it is 1474 cheaper for the network to provide lower fidelity pairs that are 1475 just above the threshold required by the application than it is 1476 to guarantee high fidelity pairs to all applications regardless 1477 of their requirements. 1479 4. Time is an expensive resource 1481 Time is not the only resource that is in short supply (memory, 1482 and communication qubits are as well), but ultimately it is the 1483 lifetime of quantum memories that imposes some of the most 1484 difficult conditions for operating an extended network of quantum 1485 nodes. Current hardware has low rates of Bell pair generation, 1486 short memory lifetimes, and access to a limited number of 1487 communication qubits. All these factors combined mean that even 1488 a short waiting queue at some node could be enough for a Bell 1489 pair to decohere or result in an end-to-end pair below an 1490 application's fidelity threshold. Therefore, managing the idle 1491 time of qubits holding live quantum states should be done 1492 carefully. Ideally by minimising the idle time, but potentially 1493 also by moving the quantum state for temporary storage to a 1494 quantum memory with a longer lifetime. 1496 5. Be flexible with regards to capabilities and limitations 1498 This goal encompasses two important points. First, the 1499 architecture should be able to function under the physical 1500 constraints imposed by the current generation hardware. Near- 1501 future hardware will have low entanglement generation rates, 1502 quantum memories able to hold a handful of qubits at best, and 1503 decoherence rates that will render many generated pairs unusable. 1505 Second, the architecture should not make it difficult to run the 1506 network over any hardware that may come along in the future. The 1507 physical capabilities of repeaters will improve and redeploying a 1508 technology is extremely challenging. 1510 7. A thought experiment inspired by classical networks 1512 To conclude, we discuss a plausible quantum network architecture 1513 inspired by MPLS. This is not an architecture proposal, but rather a 1514 thought experiment to give the reader an idea of what components are 1515 necessary for a functional quantum network. We use classical MPLS as 1516 a basis as it is well known and understood in the networking 1517 community. 1519 Creating end-to-end Bell pairs between remote end-points is a 1520 stateful distributed task that requires a lot of a-priori 1521 coordination. Therefore, a connection-oriented approach seems the 1522 most natural for quantum networks. In connection-oriented quantum 1523 networks, when two quantum application end-points wish to start 1524 creating end-to-end Bell pairs, they must first create a quantum 1525 virtual circuit (QVC). As an analogy, in MPLS networks end-points 1526 must establish a label switched path (LSP) before exchanging traffic. 1527 Connection-oriented quantum networks may also support virtual 1528 circuits with multiple end-points for creating multipartite 1529 entanglement. As an analogy, MPLS networks have the concept of 1530 multi-point LSPs for multicast. 1532 When a quantum application creates a quantum virtual circuit, it can 1533 indicate quality of service (QoS) parameters such as the required 1534 capacity in end-to-end Bell pairs per second (BPPS) and the required 1535 fidelity of the Bell pairs. As an analogy, in MPLS networks 1536 applications specify the required bandwidth in bits per second (BPS) 1537 and other constraints when they create a new LSP. 1539 Different applications will have different QoS requirements. For 1540 example, applications such as QKD, that don't need to process the 1541 entangled qubits and only need measure them and store the resulting 1542 outcome, may require a large volume of entanglement, but will be 1543 tolerant of delay and jitter for individual pairs. On the other 1544 hand, distributed/cloud quantum computing applications may need fewer 1545 entangled pairs, but instead, may need all of them to be generated in 1546 one go so that they can be processed all together before any of them 1547 decohere. 1549 Quantum networks need a routing function to compute the optimal path 1550 (i.e. the best sequence of routers and links) for each new quantum 1551 virtual circuit. The routing function may be centralized or 1552 distributed. In the latter case, the quantum network needs a 1553 distributed routing protocol. As an analogy, classical networks use 1554 routing protocols such as open shortest path first (OSPF) and 1555 intermediate-system to intermediate system (IS-IS). However, note 1556 that the definition of "shortest-path"/"least-cost" may be different 1557 in a quantum network to account for its non-classical features, such 1558 as fidelity [VanMeter13.2]. 1560 Given the very scarce availability of resources in early quantum 1561 networks, a traffic engineering function is likely to be beneficial. 1562 Without traffic engineering, quantum virtual circuits always use the 1563 shortest path. In this case, the quantum network cannot guarantee 1564 that each quantum end-point will get its Bell pairs at the required 1565 rate or fidelity. This is analogous to "best effort" service in 1566 classical networks. 1568 With traffic engineering, quantum virtual circuits choose a path that 1569 is guaranteed to have the requested resources (e.g. bandwidth in 1570 BPPS) available, taking into account the capacity of the routers and 1571 links and taking into account the resources already consumed by other 1572 virtual circuits. As an analogy, both OSPF and IS-IS have traffic 1573 engineering (TE) extensions to keep track of used and available 1574 resources, and can use constrained shortest path first (CSPF) to take 1575 resource availability and other constraints into account when 1576 computing the optimal path. 1578 The use of traffic engineering implies the use of call admission 1579 control (CAC): the network denies any virtual circuits for which it 1580 cannot guarantee the requested quality of service a-priori. Or 1581 alternatively, the network pre-empts lower priority circuits to make 1582 room for the new one. 1584 Quantum networks need a signaling function: once the path for a 1585 quantum virtual circuit has been computed, signaling is used to 1586 install the "forwarding rules" into the data plane of each quantum 1587 router on the path. The signaling may be distributed, analogous to 1588 the resource reservation protocol (RSVP) in MPLS. Or the signaling 1589 may be centralized, similar to OpenFlow. 1591 Quantum networks need an abstraction of the hardware for specifying 1592 the forwarding rules. This allows us to de-couple the control plane 1593 (routing and signaling) from the data plane (actual creation of Bell 1594 pairs). The forwarding rules are specified using abstract building 1595 blocks such as "creating local Bell pairs", "swapping Bell pairs", 1596 "distillation of Bell pairs". As an analogy, classical networks use 1597 abstractions that are based on match conditions (e.g. looking up 1598 header fields in tables) and actions (e.g. modifying fields or 1599 forwarding a packet to a specific interface). The data-plane 1600 abstractions in quantum networks will be very different from those in 1601 classical networks due to the fundamental differences in technology 1602 and the stateful nature of quantum networks. In fact, choosing the 1603 right abstractions will be one of the biggest challenges when 1604 designing interoperable quantum network protocols. 1606 In quantum networks, control plane traffic (routing and signaling 1607 messages) is exchanged over a classical channel, whereas data plane 1608 traffic (the actual Bell pair qubits) is exchanged over a separate 1609 quantum channel. This is in contrast to most classical networks, 1610 where control plane traffic and data plane traffic share the same 1611 channel and where a single packet contains both user fields and 1612 header fields. There is, however, a classical analogy to the way 1613 quantum networks work. Generalized MPLS (GMPLS) networks use 1614 separate channels for control plane traffic and data plane traffic. 1615 Furthermore, GMPLS networks support data planes where there is no 1616 such thing as data plane headers (e.g. DWDM or TDM networks). 1618 8. Security Considerations 1620 Security is listed as an explicit goal for the architecture and this 1621 issue is addressed in the section on goals. However, as this is an 1622 informational draft it does not propose any concrete mechanisms to 1623 achieve these goals. 1625 9. IANA Considerations 1627 This draft includes no request to IANA. 1629 10. Acknowledgements 1631 The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel 1632 Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang, 1633 Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG 1634 community as a whole for their very useful reviews and comments to 1635 the document. 1637 11. Informative References 1639 [Abobeih18] 1640 Abobeih, M.H., Cramer, J., Bakker, M.A., Kalb, N., 1641 Markham, M., Twitchen, D.J., and T.H. 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Zurek, "A single quantum cannot be 2003 cloned", Nature Vol. 299, Iss. 5886, pp. 802-803, 1982, 2004 . 2006 [ZOO] "The Quantum Protocol Zoo", . 2008 Authors' Addresses 2010 Wojciech Kozlowski 2011 QuTech 2012 Building 22 2013 Lorentzweg 1 2014 2628 CJ Delft 2015 Netherlands 2017 Email: w.kozlowski@tudelft.nl 2018 Stephanie Wehner 2019 QuTech 2020 Building 22 2021 Lorentzweg 1 2022 2628 CJ Delft 2023 Netherlands 2025 Email: s.d.c.wehner@tudelft.nl 2027 Rodney Van Meter 2028 Keio University 2029 5322 Endo, Kanagawa 2030 252-0882 2031 Japan 2033 Email: rdv@sfc.wide.ad.jp 2035 Bruno Rijsman 2036 Individual 2038 Email: brunorijsman@gmail.com 2040 Angela Sara Cacciapuoti 2041 University of Naples Federico II 2042 Department of Electrical Engineering and Information Technologies 2043 Claudio 21 2044 80125 Naples 2045 Italy 2047 Email: angelasara.cacciapuoti@unina.it 2049 Marcello Caleffi 2050 University of Naples Federico II 2051 Department of Electrical Engineering and Information Technologies 2052 Claudio 21 2053 80125 Naples 2054 Italy 2056 Email: marcello.caleffi@unina.it 2058 Shota Nagayama 2059 Mercari, Inc. 2060 Roppongi Hills Mori Tower 18F 2061 6-10-1 Roppongi, Minato-ku, 2062 106-6118 2063 Japan 2065 Email: shota.nagayama@mercari.com