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Checking references for intended status: Informational ---------------------------------------------------------------------------- No issues found here. Summary: 0 errors (**), 0 flaws (~~), 1 warning (==), 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: March 8, 2020 September 5, 2019 7 Architectural Principles for a Quantum Internet 8 draft-irtf-qirg-principles-01 10 Abstract 12 The vision of a quantum internet is to fundamentally enhance Internet 13 technology by enabling quantum communication between any two points 14 on Earth. To achieve this goal, a quantum network stack should be 15 built from the ground up as the physical nature of the communication 16 is fundamentally different. The first realisations of quantum 17 networks are imminent, but there is no practical proposal for how to 18 organise, utilise, and manage such networks. In this memo, we 19 attempt lay down the framework and introduce some basic architectural 20 principles for a quantum internet. This is intended for general 21 guidance and general interest, but also to provide a foundation for 22 discussion between physicists and network specialists. 24 Status of This Memo 26 This Internet-Draft is submitted in full conformance with the 27 provisions of BCP 78 and BCP 79. 29 Internet-Drafts are working documents of the Internet Engineering 30 Task Force (IETF). Note that other groups may also distribute 31 working documents as Internet-Drafts. The list of current Internet- 32 Drafts is at https://datatracker.ietf.org/drafts/current/. 34 Internet-Drafts are draft documents valid for a maximum of six months 35 and may be updated, replaced, or obsoleted by other documents at any 36 time. It is inappropriate to use Internet-Drafts as reference 37 material or to cite them other than as "work in progress." 39 This Internet-Draft will expire on March 8, 2020. 41 Copyright Notice 43 Copyright (c) 2019 IETF Trust and the persons identified as the 44 document authors. All rights reserved. 46 This document is subject to BCP 78 and the IETF Trust's Legal 47 Provisions Relating to IETF Documents 48 (https://trustee.ietf.org/license-info) in effect on the date of 49 publication of this document. Please review these documents 50 carefully, as they describe your rights and restrictions with respect 51 to this document. Code Components extracted from this document must 52 include Simplified BSD License text as described in Section 4.e of 53 the Trust Legal Provisions and are provided without warranty as 54 described in the Simplified BSD License. 56 Table of Contents 58 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 59 2. Model of communication . . . . . . . . . . . . . . . . . . . 3 60 2.1. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 3 61 2.2. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 4 62 3. Entanglement as the fundamental service . . . . . . . . . . . 5 63 4. Achieving quantum connectivity . . . . . . . . . . . . . . . 7 64 4.1. No-cloning theorem . . . . . . . . . . . . . . . . . . . 7 65 4.2. Direct transmission . . . . . . . . . . . . . . . . . . . 7 66 4.3. Bell pairs and entanglement swapping . . . . . . . . . . 8 67 4.3.1. Bell Pairs . . . . . . . . . . . . . . . . . . . . . 8 68 4.3.2. Teleportation . . . . . . . . . . . . . . . . . . . . 8 69 4.3.3. Bell Pair links and entanglement swapping . . . . . . 9 70 4.3.4. Distillation . . . . . . . . . . . . . . . . . . . . 10 71 4.4. Direct transmission vs. swapping . . . . . . . . . . . . 10 72 5. Architecture of a quantum internet . . . . . . . . . . . . . 10 73 5.1. Model of a quantum network . . . . . . . . . . . . . . . 11 74 5.2. Physical constraints . . . . . . . . . . . . . . . . . . 12 75 5.2.1. Fidelity . . . . . . . . . . . . . . . . . . . . . . 12 76 5.2.2. Memory lifetimes . . . . . . . . . . . . . . . . . . 12 77 5.2.3. Rates . . . . . . . . . . . . . . . . . . . . . . . . 13 78 5.2.4. Communication qubit . . . . . . . . . . . . . . . . . 13 79 5.2.5. Homogeneity . . . . . . . . . . . . . . . . . . . . . 13 80 5.3. Architectural principles . . . . . . . . . . . . . . . . 14 81 5.3.1. Goals of a quantum internet . . . . . . . . . . . . . 14 82 5.3.2. The principles of a quantum internet . . . . . . . . 16 83 6. Security Considerations . . . . . . . . . . . . . . . . . . . 19 84 7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 19 85 8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 19 86 9. Informative References . . . . . . . . . . . . . . . . . . . 20 87 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 21 89 1. Introduction 91 Quantum networks are distributed systems of quantum devices that 92 utilise fundamental quantum mechanical phenomena such as 93 superposition, entanglement, and quantum measurement to achieve 94 capabilities beyond what is possible with classical networks. 95 Depending on the stage of a quantum network [5] such devices may be 96 simple photonic devices capable of preparing and measuring only one 97 quantum bit (qubit) at a time, all the way to large-scale quantum 98 computers of the future. A quantum network is not meant to replace 99 classical networks, but rather form an overall hybrid classical 100 quantum network supporting new capabilities which are otherwise 101 impossible to realise. This new networking paradigm offers promise 102 for a range of new applications such as secure communications [1], 103 distributed quantum computation [2], or quantum sensor networks [3]. 104 The field of quantum communication has been a subject of active 105 research for many years and the most well-known application of 106 quantum communication, quantum key distribution (QKD) for secure 107 communications, has already been deployed at short (roughly 100km) 108 distances. 110 Fully quantum networks capable of transmitting and managing entangled 111 quantum states in order to send, receive, and manipulate distributed 112 quantum information are now imminent [4] [5]. Whilst a lot of effort 113 has gone into physically realising and connecting such devices, and 114 making improvements to their speed and error tolerance there are no 115 worked out proposals for how to run these networks. To draw an 116 analogy with a classical network, we are at a stage where we can 117 start to physically connect our devices and send data, but all 118 sending, receiving, buffer management, connection synchronisation, 119 and so on, must be managed by the application itself at what is even 120 lower than assembly level where no common interfaces yet exist. 121 Furthermore, whilst physical mechanisms for forwarding quantum states 122 exist, there are no robust protocols for managing such transmissions. 124 2. Model of communication 126 In order to understand the framework for quantum networking a basic 127 understanding of quantum information is necessary. The following 128 sections aim to introduce the bare minimum necessary to understand 129 the principles of operation of a quantum network. This exposition 130 was written with a classical networking audience in mind. It is 131 assumed that the reader has never before been exposed to any quantum 132 physics. We refer to e.g. [11] for an in-depth introduction to 133 quantum information. 135 2.1. Qubit 137 The differences between quantum computation and classical computation 138 begin at the bit-level. A classical computer operates on the binary 139 alphabet { 0, 1 }. A quantum bit, a qubit, exists over the same 140 binary space, but unlike the classical bit, it can exist in a so- 141 called superposition of the two possibilities: 143 a |0> + b |1>, 144 where |X> denotes a quantum state, here the binary 0 and 1, and the 145 coefficients a and b are complex numbers called probability 146 amplitudes. Physically, such a state can be realised using a variety 147 of different technologies such as electron spin, photon polarisation, 148 atomic energy levels, and so on. 150 Upon measurement, the qubit loses its superposition and irreversibly 151 collapses into one of the two basis states, either |0> or |1>. Which 152 of the two states it ends up in is not deterministic, but it can be 153 determined from the readout of the measurement, a classical bit, 0 or 154 1 respectively. The probability of measuring the state in the |0> 155 state is |a|^2 and similarly the probability of measuring the state 156 in the |1> state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness 157 is not due to our ignorance of the underlying mechanisms, but rather 158 it is a fundamental feature of a quantum mechanical system [6]. 160 The superposition property plays an important role in fundamental 161 gate operations on qubits. Since a qubit can exist in a 162 superposition of its basis states, the elementary quantum gates are 163 able to act on all states of the superposition at the same time. For 164 example, consider the NOT gate: 166 NOT (a |0> + b |1>) -> a |1> + b |0>. 168 2.2. Multiple qubits 170 When multiple qubits are combined in a single quantum state the space 171 of possible states grows exponentially and all these states can 172 coexist in a superposition. For example, the general form of a two- 173 qubit register is 175 a |00> + b |01> + c |10> + d |11> 177 where the coefficients have the same probability amplitude 178 interpretation as for the single qubit state. Each state represents 179 a possible outcome of a measurement of the two-qubit register. For 180 example, |01>, denotes a state in which the first qubit is in the 181 state |0> and the second is in the state |1>. 183 Performing single qubit gates affects the relevant qubit in each of 184 the superposition states. Similarly, two-qubit gates also act on all 185 the relevant superposition states, but their outcome is far more 186 interesting. 188 Consider a two-qubit register where the first qubit is in the 189 superposed state (|0> + |1>)/sqrt(2) and the other is in the 190 state |0>. This combined state can be written as: 192 (|0> + |1>)/sqrt(2) x |0> = (|00> + |10>)/sqrt(2), 194 where x denotes a tensor product (the mathematical mechanism for 195 combining quantum states together). Let us now consider the two- 196 qubit CNOT gate. The CNOT gate takes as input two qubits, a control 197 and target, and applies the NOT gate to the target if the control 198 qubit is set. The truth table looks like 200 +----+-----+ 201 | IN | OUT | 202 +----+-----+ 203 | 00 | 00 | 204 | 01 | 01 | 205 | 10 | 11 | 206 | 11 | 10 | 207 +----+-----+ 209 Now, consider performing a CNOT gate on the ensemble with the first 210 qubit being the control. We apply a two-qubit gate on all the 211 superposition states: 213 CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2). 215 What is so interesting about this two-qubit gate operation? The 216 final state is *entangled*. There is no possible way of representing 217 that quantum state as a product of two individual qubits, they are no 218 longer independent and their behaviour cannot be fully described 219 without accounting for the other qubit. The states of the two 220 individual qubits are now correlated beyond what is possible to 221 achieve classically. Neither qubit is in a definite |0> or |1> 222 state, but if we perform a measurement on either one, the outcome of 223 the partner qubit will *always* yield the exact same outcome. The 224 final state, whether it's |00> or |11>, is fundamentally random as 225 before, but the states of the two qubits following a measurement will 226 always be identical. 228 Once a measurement is performed, the two qubits are once again 229 independent. The final state is either |00> or |11> and both of 230 these states can be trivially decomposed into a product of two 231 individual qubits. The entanglement has been consumed and if the 232 same measurement is to be repeated, the entangled state must be 233 prepared again. 235 3. Entanglement as the fundamental service 237 Entanglement is the fundamental building block of quantum networks. 238 To see this, consider the state from the previous section: 240 (|00> + |11>)/sqrt(2). 242 Neither of the two qubits is in a definite |0> or |1> state and we 243 need to know the state of the entire register to be able to fully 244 describe the behaviour of the two qubits. 246 Entangled qubits have interesting non-local properties. Consider 247 sending one of the qubits to another device. This device could in 248 principle be anywhere: on the other side of the room, in a different 249 country, or even on a different planet. Provided negligible noise 250 has been introduced, the two qubits will forever remain in the 251 entangled state until a measurement is performed. The physical 252 distance does not matter at all for entanglement. 254 This lies at the heart of quantum networking, because it is possible 255 to leverage the non-classical correlations provided by entanglement 256 in order to design completely new types of application protocols that 257 are not possible to achieve with just classical communication. 258 Examples of such applications are quantum cryptography, blind quantum 259 computation, or distributed quantum computation. 261 Entanglement has two very special features from which one can derive 262 some intuition about the types of applications enabled by a quantum 263 network. 265 The first stems from the fact that entanglement enables stronger than 266 classical correlations, leading to opportunities for tasks that 267 require coordination. As a trivial example consider the problem of 268 consensus between two nodes who want to agree on the value of a 269 single bit. They can use the quantum network to prepare the state 270 (|00> + |11>)/sqrt(2) with each node holding one of the two qubits. 271 Once any of the two nodes performs a measurement the state of the two 272 qubits collapses to either |00> or |11> so whilst the outcome is 273 random and does not exist before measurement, the two nodes will 274 always measure the same value. We can also build the more general 275 multi-qubit state (|00...> + |11...>)/sqrt(2) and perform the same 276 algorithm between an arbitrary number of nodes. These stronger than 277 classical correlations generalise to more complicated measurement 278 schemes as well. 280 The second feature of entanglement is that it cannot be shared, in 281 the sense that if two qubits are maximally entangled with each other, 282 than it is physically impossible for any other system to have any 283 share of this entanglement. Hence, entanglement forms a sort of 284 private and inherently untappable connection between two nodes once 285 established. 287 It is impossible to entangle two qubits without ever having them 288 directly interact with each other (e.g. by performing a local two- 289 qubit gate, such as the CNOT). A local - or mediated - interaction 290 is necessary to create entanglement and thus such states cannot be 291 created between two quantum nodes that cannot transmit quantum states 292 to each other. Therefore, it is the transmission of qubits that 293 draws the line between a genuine quantum network and a collection of 294 quantum computers connected over a classical network. 296 A quantum network is defined as a collection of nodes that is able to 297 exchange qubits and distribute entangled states amongst themselves. 298 A quantum node that is able only to communicate classically with 299 another quantum node is not a member of a quantum network. 301 More complex services and applications can be built on top of 302 entangled states distributed by the network, see e.g. [5]> 304 4. Achieving quantum connectivity 306 4.1. No-cloning theorem 308 To build a network we must first physically connect all the nodes 309 with quantum channels that enable them to distribute the 310 entanglement. Unfortunately, our ability to transfer quantum states 311 is complicated by the no-cloning theorem. 313 The no-cloning theorem states that it is impossible to create an 314 identical copy of an arbitrary unknown quantum state. Since 315 performing a measurement on a quantum state destroys its 316 superposition, there is no practical way of learning the exact state 317 of a qubit in an unknown state. Therefore, it is impossible to use 318 the same mechanisms that worked for classical networks for signal 319 amplification, retransmission, and so on as they all rely on the 320 ability to copy the underlying data. Since any physical channel will 321 always be lossy, connecting nodes within a quantum network is a 322 challenging endeavour and its architecture must at its core address 323 this very issue. 325 4.2. Direct transmission 327 The most straightforward way to distribute an entangled state is to 328 simply transmit one of the qubits directly to the other end across a 329 series of nodes while performing sufficient forward quantum error 330 correction to bring losses down to an acceptable level. Despite the 331 no-cloning theorem and the inability to directly measure a quantum 332 state error-correcting mechanisms for quantum communication exist 333 [7]. However, even in the most optimistic scenarios the hardware 334 requirements to fault-tolerantly transmit a single qubit are far 335 beyond near-term capabilities. Nevertheless, due to the promise of 336 fault-tolerance and direct transmission's favourable poly-logarithmic 337 scaling with distance, it may eventually become a desirable method 338 for entanglement distribution. 340 4.3. Bell pairs and entanglement swapping 342 4.3.1. Bell Pairs 344 An alternative relies on the observation that we do not need to be 345 able to distribute any arbitrary entangled quantum state. We only 346 need to be able to distribute any one of what are known as the Bell 347 Pair states. Bell Pair states are the entangled two-qubit states: 349 |00> + |11>, 350 |00> - |11>, 351 |01> + |10>, 352 |01> - |10>, 354 where the constant 1/sqrt(2) normalisation factor has been ignored 355 for clarity. Any of the four Bell Pair state above will do as it is 356 possible to transform any Bell Pair into another Bell Pair with local 357 operations performed on only one of the qubits. That is, either of 358 the nodes that hold the two qubits of the Bell Pair can apply a 359 series of single qubit gates to just their qubit in order to 360 transform the ensemble between the different variants. 362 Distributing a Bell Pair between two nodes is much easier than 363 transmitting an arbitrary quantum state over a network. Since the 364 state is known handling errors becomes easier and small-scale error- 365 correction (such as entanglement distillation) combined with 366 reattempts becomes a valid strategy. 368 The reason for using Bell Pairs specifically as opposed to any other 369 two-qubit state, is that they are the maximally entangled two-qubit 370 set of basis states. Maximal entanglement means that these states 371 have the strongest non-classical correlations of all possible two- 372 qubit states. Furthermore, since single-qubit local operations can 373 never increase entanglement, less entangled states would impose some 374 constraints on distributed quantum algorithms. This makes Bell Pairs 375 particularly useful as a generic building block for distributed 376 quantum applications. 378 4.3.2. Teleportation 380 The observation that we only need to be able to distribute Bell Pairs 381 relies on the fact that this enables the distribution of any other 382 arbitrary entangled state. This can be achieved via quantum state 383 teleportation. Quantum state teleportation consumes an unknown 384 quantum state that we want to transmit and recreates it at the 385 desired destination. This does not violate the no-cloning theorem as 386 the original state is destroyed in the process 388 To achieve this, a Bell Pair needs to be distributed between the 389 source and destination before teleportation commences. The source 390 then entangles the transmission qubit with its end of the Bell Pair 391 and performs a measurement. This consumes the Bell Pair's 392 entanglement turning the source and destination qubits into 393 independent states. The measurements yields two classical bits which 394 the source sends to the destination over a classical channel. Based 395 on the value of the received two classical bits, the destination 396 performs one of four possible operations on its end of the Bell Pair, 397 which results in a clone of the unknown quantum state of the 398 transmission qubit. 400 The unknown quantum state that was transmitted never entered the 401 network itself. Therefore, the network needs to only be able to 402 reliably produce Bell Pairs between any two nodes in the network. 404 4.3.3. Bell Pair links and entanglement swapping 406 Reducing the problem of quantum connectivity to one of generating a 407 Bell Pair has facilitated the problem, but it has not solved it. 409 The technology to generate a Bell Pair between two directly connected 410 quantum nodes, store the qubits, and perform teleportation, already 411 exists and has been demonstrated in laboratory conditions [8]. 412 Interestingly, neither of the two qubits of the pair need to be 413 transmitted any further. 415 A Bell Pair between any two nodes in the network can be constructed 416 from Bell Pairs generated along each individual link on the path 417 between the two end-points. Each node along the path can consume the 418 two Bell Pairs on the two links that it is connected to in order to 419 produce a new Bell Pair between the two far ends. This process is 420 known as entanglement swapping. Pictorially it can be represented as 421 follows: 423 x~~~~~~~~~~~~~x x~~~~~~~~~~~~~x 424 [ ]-----------[ ]-----------[ ] 426 where x~~x denotes a Bell Pair with individual qubits represented by 427 x, -- denotes a quantum link, and [ ] denotes a node. The diagram 428 above represents the situation after the middle node has generated a 429 Bell Pair with two of its directly connected neighbours. Now, the 430 middle node performs an entanglement swap operation (the exact 431 details of the mechanism are beyond the scope of this memo). This 432 operation consumes the two Bell Pairs and produces a new Bell Pair 433 between the two far ends of this three-node network as follows: 435 x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x 436 [ ]-----------[ ]-----------[ ] 438 The outcome is guaranteed to be a Bell Pair between the two end 439 nodes, but which of the four possible Bell Pairs is produced is not 440 deterministic. However, the middle node will know which one was 441 produced as the entanglement swap is a measurement operation that 442 yields two classical bits. The final state can be inferred from this 443 two-bit readout. Therefore, the middle node needs only to 444 communicate the outcome over a classical channel to one or both ends 445 who can apply a correction to transform the pair into any of its 446 other forms (if so desired). 448 4.3.4. Distillation 450 Neither the generation of Bell Pairs or the swapping operations are 451 lossless operations. Therefore, with each link and each swap the 452 quality of the state degrades. However, it is possible to create 453 higher quality Bell Pair states from two or more lower quality Bell 454 Pair states through a process called distillation. Therefore, once 455 the quality loss over a given distance become prohibitive, additional 456 redundancy may be used to restore the state quality. 458 4.4. Direct transmission vs. swapping 460 Direct state transmission whilst simpler conceptually is much more 461 demanding to implement reliably in practice which means that any 462 near-term practical realisation is more likely to succeed if it is 463 based on the Bell Pair and entanglement swapping architecture. This 464 is the architecture that we will focus on in the rest of this memo 465 for practical reasons. 467 Nevertheless, the direct transmission proposal may be relevant in the 468 future as it does enable the fault-tolerant transmission of unknown 469 quantum states. It might even be beneficial to utilise a hybrid 470 approach that combines the fault-tolerance of direct transmission 471 with the generic nature of Bell Pairs which lends itself to 472 paralellisation and resource provisioning. 474 5. Architecture of a quantum internet 475 5.1. Model of a quantum network 477 A generic quantum network of three nodes could be represented as 479 | App |--------------------CC--------------------| App | 480 || || 481 ------ ------ ------ 482 | QNet |-------CC-------| QNet |-------CC-------| QNet | 483 ------ ------ ------ 484 \ Bell Pair Gen. / SWAP \ Bell Pair Gen. / 485 ---------------- ---------------- 487 Where "App" is some application running over a quantum network, 488 --CC-- denote classical communication links (e.g. over the public 489 Internet or a private LAN), and "QNet" is a generic network stack. 490 Architectures for the network stack have been proposed already 491 [9][10], but their discussion is beyond the scope of this memo. 492 However, they all map onto this generic diagram. Nodes within a 493 quantum network that are capable of performing the entanglement swap 494 operation are often referred to as quantum repeaters and we shall 495 adopt this terminology from this point on. End-hosts connecting at 496 the edge of the network are not necessarily repeaters themselves. 498 The key message here is that a network stack relies on the hardware 499 being able to provide two services: Bell Pair generation across a 500 link, and swap operation. In any network model it is assumed that 501 the physical device is capable of providing both of these services 502 and offers a suitable interface for their usage. 504 Strictly speaking (under idealised conditions) quantum memories are 505 not needed for a functional quantum network as long as the network is 506 able to simultaneously generate all the Bell Pairs, swap the 507 entanglement, and deliver the final Bell Pair to the application in a 508 usable form. However, realistically, to be able to provide the two 509 services above, the hardware will also need to be able to store the 510 qubits in memory which is highly non-trivial. 512 Furthermore, it is also assumed that the applications are able to 513 communicate classically, and that the nodes themselves are also 514 connected over some logical classical channel. The classical and 515 quantum links do not have to coincide. The classical messaging may 516 take a completely different path to the quantum channel as long as 517 the latency characteristics meet the requirements of the control 518 protocol. 520 5.2. Physical constraints 522 The model above has effectively abstracted away the particulars of 523 the hardware implementation. However, certain physical constraints 524 need to be considered in order to build a practical network. Some of 525 these are fundamental constraints and no matter how much the 526 technology improves, they will always need to be addressed. Others 527 are artefacts of the early stages of a new technology. We here 528 consider a highly abstract scenario and refer to [5] for pointers to 529 the physics literature. 531 5.2.1. Fidelity 533 The quality of a quantum state is described by a physical quantity 534 called fidelity, that takes a value between 0 and 1 (higher is 535 better). Fidelity is the measure of how close a quantum state is to 536 the quantum state we desire it to be in. It expresses the 537 probability that one state will pass a test to identify as the other. 539 Fidelity is an important property of a quantum system that stems from 540 the fact that no physical operation is perfect. Furthermore, 541 applications will in general require the fidelity of a quantum state 542 to be above some minimum threshold in order to guarantee the 543 correctness of their algorithm and it is the responsibility of the 544 network to provide such a state. 546 Additionally, entanglement swapping operations, even if perfect, lead 547 to a further reduction in the fidelity of the final state. Two 548 imperfect Bell Pairs when combined will produce a slightly worse Bell 549 Pair. Whilst distillation is one of the available mechanisms to 550 correct for these errors it requires additional Bell Pairs to be 551 produced. There will be a trade-off between how much distillation is 552 to be done versus what fidelity is acceptable. 554 This is a fundamental constraint as perfect noiseless operations and 555 lossless communication channels are unachievable. Therefore, no Bell 556 Pair will be generated with perfect fidelity and the network must 557 account for this. 559 5.2.2. Memory lifetimes 561 In addition to discrete operations being imperfect, storing a qubit 562 in memory is also highly non-trivial. The main difficulty in 563 achieving persistent storage is that it is extremely challenging to 564 isolate a quantum system from the environment. The environment 565 introduces an uncontrollable source of noise into the system which 566 affects the fidelity of the state. This process is known as 567 decoherence. Eventually, the state has to be discarded once its 568 fidelity degrades too much. 570 The memory lifetime depends on the particular physical setup, but the 571 highest achievable values currently are on the order of seconds. 572 These values have increased tremendously over the lifetime of the 573 different technologies and are bound to keep increasing. However, if 574 quantum networks are to be realised in the near future, they need to 575 be able to handle short memory lifetimes. An architecture that 576 handles short lifetimes may also be more cost-efficient in the 577 future. 579 5.2.3. Rates 581 Entanglement generation on a link between two connected nodes is not 582 a very efficient process and it requires many attempts to succeed. A 583 fast repetition rate for Bell Pair generation is achievable, but only 584 one in a few thousands will succeed. Currently, the highest 585 achievable rates of success between nodes capable of storing the 586 resulting qubits are of the order of 10 Hz. Combined with short 587 memory lifetimes this leads to very tight timing windows to build up 588 network-wide connectivity. Achievable rates are likely to increase 589 with time, but just like with quantum memories, it may be more cost- 590 efficient in the future to provide low-rate links in some parts of 591 the network. 593 5.2.4. Communication qubit 595 Most physical architectures capable of storing qubits are only able 596 to generate entanglement using only a subset of its available qubits 597 called communication qubits. Once a Bell Pair has been generated 598 using a communication qubit, its state can be transferred into 599 memory. This may impose additional limitations on the network. In 600 particular if a given node has only one communication qubit it cannot 601 simultaneously generate Bell Pairs over two links. It must generate 602 entanglement over the links one at a time. 604 5.2.5. Homogeneity 606 Currently all hardware implementations are homogeneous and they do 607 not interface with each other. In general, it is very challenging to 608 combine different quantum information processing technologies at 609 present. Coupling different technologies with each other is of great 610 interest as it may help overcome the weaknesses of the different 611 implementations, but this may take a long time to be realised with 612 high reliability and thus is not a near-term goal. 614 5.3. Architectural principles 616 Given that the most practical way of realising quantum network 617 connectivity is using Bell Pair and entanglement swapping repeater 618 technology what sort of principles should guide us in assembling such 619 networks such that they are functional, robust, efficient, and most 620 importantly: they work. Furthermore, how do we design networks so 621 that they work under the constraints imposed by the hardware 622 available today, but do not impose unnecessary burden on future 623 technology. Redeploying network technology is a non-trivial process. 625 As this is a completely new technology that is likely to see many 626 iterations over its lifetime, this memo must not serve as a 627 definitive set of rules, but merely as a general set of recommended 628 guidelines based on principles and observations made by the 629 community. The benefit of having a community built document at this 630 early stage is that expertise in both quantum information and network 631 architecture is needed in order to successfully build a quantum 632 internet. 634 5.3.1. Goals of a quantum internet 636 When outlining any set of principles we must ask ourselves what goals 637 do we want to achieve as inevitably trade-offs must be made. So what 638 sort of goals should drive a quantum network architecture? The 639 following list has been inspired by the history of the classical 640 Internet, but it will inevitably evolve with time and the needs of 641 its users. The goals are listed in order of priority which in itself 642 may also evolve as the community learns more about the technology. 644 1. Support distributed quantum applications 646 The primary purpose of a quantum internet is to run distributed 647 quantum protocols and it is of utmost importance that they can 648 run well and efficiently. Therefore, the needs of quantum 649 applications should always be considered first. The requirements 650 for different applications can be found in [5]. 652 If a network is able to distribute entanglement it is officially 653 quantum. However, if it is unable to distribute these states 654 with a sufficiently high fidelity at a reasonable rate for a 655 majority of potential applications it is not practical. 657 2. Support tomorrow's distributed quantum applications 659 There are many applications already proposed to run over a 660 quantum internet. However, more algorithms will be invented as 661 the community grows as well as the robustness and the reliability 662 of the technology. Any proposed architecture should not 663 constrain the capabilities of the network for short-term benefit. 665 3. Hardware heterogeneity 667 There are multiple proposals for realising practical quantum 668 repeaters and they all have their advantages and disadvantages. 669 It is also very likely that the most optimal technologies in the 670 future will be hybrid combinations of the many different 671 solutions currently under development. It should be an explicit 672 goal of the architecture to allow for a large variety of hardware 673 implementations. 675 4. Be flexible with regards to hardware capabilities and limitations 677 This goal encompasses two important points. First, the 678 architecture should be able to function under the physical 679 constraints imposed by the current generation hardware. Second, 680 it should not make it difficult to run the network over any 681 hardware that may come along in the future. The physical 682 capabilities of repeaters will improve and redeploying a 683 technology is extremely challenging. 685 5. Security 687 Whilst the priority for the first quantum networks should be to 688 simply work, we cannot forget that ultimately they have to also 689 be secure. This has implications for the physical realisations 690 (do they satisfy the idealised theoretical models) and also the 691 design of the control stack. 693 It is actually difficult to guarantee security at the network 694 level and even if the network did provide such guarantees, the 695 application would still need to perform its own verification 696 similarly to how one ensures end-to-end security in classical 697 networks. 699 It turns out that as long as the underlying implementation 700 corresponds to (or sufficiently approximates) theoretical models 701 of quantum cryptography, quantum cryptographic protocols do not 702 need the network to provide any guarantees about the 703 authenticity, confidentiality, or integrity of the transmitted 704 qubits or the generated entanglement. Instead, applications such 705 as QKD establish such guarantees using the classical network in 706 conjunction with he quantum one. This is much easier than 707 demanding that the network deliver secure entanglement, which 708 indeed is not needed for quantum applications. 710 Nevertheless, control protocols themselves should be security 711 aware in order to protect the operation of the network itself and 712 limit disruption. 714 6. Availability and resilience 716 A practical and usable network is able to continue to operate 717 despite losses and failures, and will be robust to malicious 718 actors trying to disable connectivity. These may be simply 719 considered different aspects of security, but it is worthwhile to 720 address them explicitly at the architectural level already. 722 7. Easy to manage and monitor 724 Quantum networks rely on complex physical phenomena and require 725 hardware that is challenging to build. Furthermore, the quantum 726 resources will at first be very scarce and potentially very 727 expensive. This entails a need for a robust management solution. 728 It is important that a good management solution needs to come 729 with adequate monitoring capabilities. 731 Good management solutions may also be key to optimising the 732 networks which in turn may be crucial in making them economically 733 feasible. Unlike user data that is transmitted over classical 734 networks, quantum networks only need to generate generic Bell 735 Pairs. This leaves a lot of room for pre-allocating resources in 736 an efficient manner. 738 5.3.2. The principles of a quantum internet 740 The principles support the goals, but are not goals themselves. The 741 goals define what we want to build and the principles provide a 742 guideline in how we might achieve this. The goals will also be the 743 foundation for defining any metric of success for a network 744 architecture, whereas the principles in themselves do not distinguish 745 between success and failure. For more information about design 746 considerations for quantum networks see [9] [10] . 748 1. Bell Pairs are the fundamental building block 750 The key service that a quantum network provides is the 751 distribution of entanglement between the nodes in a network. 752 This point additionally specifies that the entanglement is 753 primarily distributed in the form of the entangled Bell Pair 754 states which should be used as a building block in providing 755 other services, including more complex entangled states. 757 2. Fidelity is part of the service 758 In addition to being able to deliver Bell Pairs to the 759 communication end-points, the Bell Pairs must be of sufficient 760 fidelity. Unlike in classical networks where errors should 761 essentially be eliminated for most application protocols, many 762 quantum applications only need imperfect entanglement to 763 function. However, different applications will have different 764 requirements for what fidelity they can work with. It is the 765 network's responsibility to balance the resource usage with 766 respect to the application's requirements. It may be that it is 767 cheaper for the network to provide lower fidelity pairs that are 768 just above the threshold required by the application than it is 769 to guarantee high fidelity pairs to all applications regardless 770 of their requirements. 772 3. Bell Pairs are indistinguishable 774 Any two Bell Pairs between the same two nodes are 775 indistinguishable for the purposes of an application provided 776 they both satisfy its required fidelity threshold. This point is 777 crucial in enabling the reuse of resources of a network and for 778 the purposes of provisioning resources to meet application 779 demand. However, the qubits that make up the pair themselves are 780 not indistinguishable and the two nodes operating on a pair must 781 coordinate to make sure they are operating on qubits that belong 782 to the same Bell Pair. 784 4. Time as an expensive resource 786 With the current technology, time is the most expensive resource. 787 It is not the only resource that is in short supply (memory, and 788 communication qubits are as well), but ultimately it is the 789 lifetime of quantum memories that imposes the most difficult 790 conditions for operating an extended network of quantum nodes. 791 Current hardware has low rates of Bell Pair generation, short 792 memory lifetimes, and access to a limited number of communication 793 qubits. All these factors combined mean that even a short 794 waiting queue at some node could be enough for the Bell Pairs to 795 decohere. 797 However, time is only expensive once quantum operations are 798 underway. If no quantum operations are currently being processed 799 then the network can use this time to prepare and provision 800 resources. 802 As hardware improves, the need for carefully timing quantum 803 operations may become smaller. It is currently unknown what the 804 cost of these improvements will be, but it is conceivable that 805 there is value in having relatively cheap and undemanding links 806 connected at the edges of a network which will have very short 807 memory lifetimes and low rates of Bell Pair generation. 809 5. Limit classical communication 811 This point offers a practical guideline to the issue of timing. 812 A bottleneck in many quantum networked algorithms is the 813 classical communication needed between quantum operations to 814 synchronise state. Ideally, classical control mechanisms that 815 require increased memory lifetimes should be avoided. 817 For example, some quantum protocols may need to perform a 818 correction for the random outcome of a quantum measurement. For 819 this, they will block the state from further operations until a 820 classical message is received with the information necessary to 821 perform the correction. The time during which the quantum state 822 is blocked is effectively wasted. It reduces the time available 823 for subsequent operations possibly rendering the state useless 824 for an application. 826 Trade-offs that allow a protocol to limit the number of blocking 827 classical communication rounds once quantum operations have 828 commenced will in general be worth considering. 830 6. Parallelise quantum operations 832 A further point to address the issue of timing constraints in the 833 network. The Bell Pairs on the individual links need not be 834 generated one after another along the path between the 835 communication end-points. The order does not matter at all. 836 Furthermore, the order of the swap operations is flexible as long 837 as they don't reduce the fidelity too much. Parallelising these 838 operations is key to optimising quantum protocols. 840 7. Avoid time-based coordination when possible 842 A solution to timing constraints is to synchronise clocks and 843 agree on the timing of events. However, such solutions have 844 several downsides. Whilst network clock synchronisation may be 845 accurate enough for certain purposes it introduces an additional 846 element of complexity, especially when multiple nodes in 847 different networks must be synchronised. Furthermore, clock 848 synchronisation will never be perfect and it is conceivable that 849 hardware capabilities advance so much that time-based mechanisms 850 under-utilise resources in the more efficient parts of the 851 network. 853 Nevertheless, it may not be possible to avoid clocks, but such 854 solutions should be adequately justified. 856 8. Pre-allocate resources 858 Regardless of what application is running over the network it 859 will have the same needs as any other application: a number of 860 Bell Pairs of sufficient fidelity. Whilst the fidelity is a 861 variable number, the indistinguishability of Bell Pairs means 862 that there is lots of flexibility in how a network may provision 863 resources to meet demand. The additional timing constraints mean 864 that pre-allocation of resources will be central to a usable 865 quantum network. 867 6. Security Considerations 869 Even though no user data enters a quantum network security is listed 870 as an explicit goal for the architecture and this issue is addressed 871 in the section on goals. Even though user data doesn't enter the 872 network, it is still possible to attack the control protocols and 873 violate the authenticity, confidentiality, and integrity of 874 communication. However, as this is an informational memo it does not 875 propose any concrete mechanisms to achieve these goals. 877 In summary: 879 As long as the underlying implementation corresponds to (or 880 sufficiently approximates) theoretical models of quantum 881 cryptography, quantum cryptographic protocols do not need the network 882 to provide any guarantees about the authenticity, confidentiality, or 883 integrity of the transmitted qubits or the generated entanglement. 884 Instead, applications such as QKD establish such guarantees using the 885 classical network in conjunction with he quantum one. This is much 886 easier than demanding that the network deliver secure entanglement. 888 7. IANA Considerations 890 This memo includes no request to IANA. 892 8. Acknowledgements 894 The authors of this memo acknowledge funding received from the EU 895 Flagship on Quantum Technologies through Quantum Internet Alliance 896 project. 898 The authors would further like to acknowledge Carlo Delle Donne, 899 Matthew Skrzypczyk, and Axel Dahlberg for useful discussions on this 900 topic prior to the submission of this memo. 902 9. Informative References 904 [1] Bennett, C. and G. Brassard, "Quantum cryptography: Public 905 key distribution and coin tossing", Theoretical Computer 906 Science 560, 7-11, 2014, 907 . 909 [2] Crepeau, C., Gottesman, D., and A. Smith, "Secure multi- 910 party quantum computation. Proceedings of Symposium on 911 Theory of Computing", Proceedings of Symposium on Theory 912 of Computing , 2002, 913 . 915 [3] Giovanetti, V., Lloyd, S., and L. Maccone, "Quantum- 916 enhanced measurements: beating the standard quantum 917 limit", Science 306(5700), 1330-1336, 2004, 918 . 920 [4] Castelvecchi, D., "The Quantum Internet has arrived (and 921 it hasn't)", Nature 554, 289-292, 2018, 922 . 924 [5] Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet: 925 A vision for the road ahead", Science 362, 6412, 2018, 926 . 929 [6] Aspect, A., Grangier, P., and G. Roger, "Experimental 930 Tests of Realistic Local Theories via Bell's Theorem", 931 Phys. Rev. Lett. 47 (7): 460-463, 1981, 932 . 935 [7] Muralidharan, S., Kim, J., Lutkenhaus, N., Lukin, M., and 936 L. Jiang, "Ultrafast and Fault-Tolerant Quantum 937 Communication across Long Distances", Phys. Rev. Lett. 112 938 (25-27), 250501, 2014, . 940 [8] Humphreys, P., Kalb, N., Morits, J., Schouten, R., 941 Vermeulen, R., Twitchen, D., Markham, M., and R. Hanson, 942 "Deterministic delivery of remote entanglement on a 943 quantum network", Nature 558, 268-273, 2018, 944 . 946 [9] Meter, R. and J. Touch, "Designing quantum repeater 947 networks", IEEE Communications Magazine 51, 64-71, 2013, 948 . 950 [10] Dahlberg, A., Skrzypczyk, M., Coopmans, T., Wubben, L., 951 Rozpedek, F., Pompili, M., Stolk, A., Pawelczak, P., 952 Knegjens, R., de Oliveira Filho, J., Hanson, R., and S. 953 Wehner, "A Link Layer Protocol for Quantum Networks", 954 arXiv 1903.09778, 2019, 955 . 957 [11] Nielsen, M. and I. Chuang, "Quantum Computation and 958 Quantum Information", Cambridge University Press , 2011. 960 Authors' Addresses 962 Wojciech Kozlowski 963 QuTech 964 Building 22 965 Lorentzweg 1 966 Delft 2628 CJ 967 Netherlands 969 Email: w.kozlowski@tudelft.nl 971 Stephanie Wehner 972 QuTech 973 Building 22 974 Lorentzweg 1 975 Delft 2628 CJ 976 Netherlands 978 Email: S.D.C.Wehner@tudelft.nl