idnits 2.17.1 draft-irtf-qirg-principles-06.txt: Checking boilerplate required by RFC 5378 and the IETF Trust (see https://trustee.ietf.org/license-info): ---------------------------------------------------------------------------- No issues found here. Checking nits according to https://www.ietf.org/id-info/1id-guidelines.txt: ---------------------------------------------------------------------------- No issues found here. Checking nits according to https://www.ietf.org/id-info/checklist : ---------------------------------------------------------------------------- No issues found here. Miscellaneous warnings: ---------------------------------------------------------------------------- == The copyright year in the IETF Trust and authors Copyright Line does not match the current year -- The document date (February 19, 2021) is 1155 days in the past. Is this intentional? Checking references for intended status: Informational ---------------------------------------------------------------------------- == Outdated reference: A later version (-19) exists of draft-irtf-qirg-quantum-internet-use-cases-04 Summary: 0 errors (**), 0 flaws (~~), 2 warnings (==), 1 comment (--).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: August 23, 2021 R. Van Meter 6 Keio University 7 B. Rijsman 8 Individual 9 A. S. Cacciapuoti 10 M. Caleffi 11 University of Naples Federico II 12 S. Nagayama 13 Mercari, Inc. 14 February 19, 2021 16 Architectural Principles for a Quantum Internet 17 draft-irtf-qirg-principles-06 19 Abstract 21 The vision of a quantum internet is to fundamentally enhance Internet 22 technology by enabling quantum communication between any two points 23 on Earth. To achieve this goal, a quantum network stack should be 24 built from the ground up to account for the fundamentally new 25 properties of quantum entanglement. The first realisations of 26 quantum networks are imminent, but there is no practical proposal for 27 how to organise, utilise, and manage such networks. In this memo, we 28 attempt to lay down the framework and introduce some basic 29 architectural principles for a quantum internet. This is intended 30 for general guidance and general interest, but also to provide a 31 foundation for discussion between physicists and network specialists. 33 Status of This Memo 35 This Internet-Draft is submitted in full conformance with the 36 provisions of BCP 78 and BCP 79. 38 Internet-Drafts are working documents of the Internet Engineering 39 Task Force (IETF). Note that other groups may also distribute 40 working documents as Internet-Drafts. The list of current Internet- 41 Drafts is at https://datatracker.ietf.org/drafts/current/. 43 Internet-Drafts are draft documents valid for a maximum of six months 44 and may be updated, replaced, or obsoleted by other documents at any 45 time. It is inappropriate to use Internet-Drafts as reference 46 material or to cite them other than as "work in progress." 48 This Internet-Draft will expire on August 23, 2021. 50 Copyright Notice 52 Copyright (c) 2021 IETF Trust and the persons identified as the 53 document authors. All rights reserved. 55 This document is subject to BCP 78 and the IETF Trust's Legal 56 Provisions Relating to IETF Documents 57 (https://trustee.ietf.org/license-info) in effect on the date of 58 publication of this document. Please review these documents 59 carefully, as they describe your rights and restrictions with respect 60 to this document. Code Components extracted from this document must 61 include Simplified BSD License text as described in Section 4.e of 62 the Trust Legal Provisions and are provided without warranty as 63 described in the Simplified BSD License. 65 Table of Contents 67 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 68 2. Quantum information . . . . . . . . . . . . . . . . . . . . . 4 69 2.1. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 4 70 2.2. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 5 71 3. Entanglement as the fundamental resource . . . . . . . . . . 6 72 4. Achieving quantum connectivity . . . . . . . . . . . . . . . 7 73 4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 8 74 4.1.1. The measurement problem . . . . . . . . . . . . . . . 8 75 4.1.2. No-cloning theorem . . . . . . . . . . . . . . . . . 8 76 4.1.3. Fidelity . . . . . . . . . . . . . . . . . . . . . . 8 77 4.1.4. Inadequacy of direct transmission . . . . . . . . . . 9 78 4.2. Bell pairs . . . . . . . . . . . . . . . . . . . . . . . 9 79 4.3. Teleportation . . . . . . . . . . . . . . . . . . . . . . 10 80 4.4. The life cycle of entanglement . . . . . . . . . . . . . 11 81 4.4.1. Elementary link generation . . . . . . . . . . . . . 11 82 4.4.2. Entanglement swapping . . . . . . . . . . . . . . . . 12 83 4.4.3. Error Management . . . . . . . . . . . . . . . . . . 13 84 4.4.4. Delivery . . . . . . . . . . . . . . . . . . . . . . 16 85 5. Architecture of a quantum internet . . . . . . . . . . . . . 16 86 5.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 16 87 5.2. Classical communication . . . . . . . . . . . . . . . . . 18 88 5.3. Abstract model of the network . . . . . . . . . . . . . . 19 89 5.3.1. The control and data planes . . . . . . . . . . . . . 19 90 5.3.2. Elements of a quantum network . . . . . . . . . . . . 19 91 5.3.3. Putting it all together . . . . . . . . . . . . . . . 21 92 5.4. Network boundaries . . . . . . . . . . . . . . . . . . . 22 93 5.4.1. Boundaries between different physical architectures . 22 94 5.4.2. Boundaries between different administrative regions . 22 95 5.4.3. Boundaries between different error management schemes 22 96 5.5. Physical constraints . . . . . . . . . . . . . . . . . . 23 97 5.5.1. Memory lifetimes . . . . . . . . . . . . . . . . . . 23 98 5.5.2. Rates . . . . . . . . . . . . . . . . . . . . . . . . 23 99 5.5.3. Communication qubits . . . . . . . . . . . . . . . . 24 100 5.5.4. Homogeneity . . . . . . . . . . . . . . . . . . . . . 24 101 6. Architectural principles . . . . . . . . . . . . . . . . . . 24 102 6.1. Goals of a quantum internet . . . . . . . . . . . . . . . 24 103 6.2. The principles of a quantum internet . . . . . . . . . . 27 104 7. A thought experiment inspired by classical networks . . . . . 29 105 8. Security Considerations . . . . . . . . . . . . . . . . . . . 31 106 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 31 107 10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 31 108 11. Informative References . . . . . . . . . . . . . . . . . . . 32 109 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 36 111 1. Introduction 113 Quantum networks are distributed systems of quantum devices that 114 utilise fundamental quantum mechanical phenomena such as 115 superposition, entanglement, and quantum measurement to achieve 116 capabilities beyond what is possible with non-quantum (classical) 117 networks [37]. Depending on the stage of a quantum network [8] such 118 devices may range from simple photonic devices capable of preparing 119 and measuring only one quantum bit (qubit) at a time all the way to 120 large-scale quantum computers of the future. A quantum network is 121 not meant to replace classical networks, but rather form an overall 122 hybrid classical-quantum network supporting new capabilities which 123 are otherwise impossible to realise [24]. 125 This new networking paradigm offers promise for a range of new 126 applications such as secure communications [3] [4], distributed 127 quantum computation [5], secure quantum computing in the cloud [28], 128 quantum-enhanced measurement networks [6], or higher-precision, long- 129 baseline telescopes [34]. The field of quantum communication has 130 been a subject of active research for many years and the most well- 131 known application of quantum communication, quantum key distribution 132 (QKD) for secure communications, has already been deployed at short 133 (roughly 100km) distances [26] [25]. 135 Fully quantum networks capable of transmitting and managing entangled 136 quantum states in order to send, receive, and manipulate distributed 137 quantum information are now imminent [7] [8]. Whilst a lot of effort 138 has gone into physically realising and connecting such devices [27], 139 and making improvements to their speed and error tolerance, there are 140 no worked out proposals for how to run these networks. To draw an 141 analogy with a classical network, we are at a stage where we can 142 start to physically connect our devices and send data, but all 143 sending, receiving, buffer management, connection synchronisation, 144 and so on, must be managed by the application itself at a level below 145 conventional assembly language, where no common interfaces yet exist. 147 Furthermore, whilst physical mechanisms for transmitting quantum 148 states exist, there are no robust protocols for managing such 149 transmissions. 151 2. Quantum information 153 In order to understand the framework for quantum networking, a basic 154 understanding of quantum information is necessary. The following 155 sections aim to introduce the bare minimum necessary to understand 156 the principles of operation of a quantum network. This exposition 157 was written with a classical networking audience in mind. It is 158 assumed that the reader has never before been exposed to any quantum 159 physics. We refer to e.g. [15] [16] for an in-depth introduction to 160 quantum information. 162 2.1. Qubit 164 The differences between quantum computation and classical computation 165 begin at the bit-level. A classical computer operates on the binary 166 alphabet { 0, 1 }. A quantum bit, called a qubit, exists over the 167 same binary space, but unlike the classical bit, it can exist in a 168 superposition of the two possibilities: 170 a |0> + b |1>, 172 where |X> is Dirac's ket notation for a quantum state, here the 173 binary 0 and 1, and the coefficients a and b are complex numbers 174 called probability amplitudes. Physically, such a state can be 175 realised using a variety of different technologies such as electron 176 spin, photon polarisation, atomic energy levels, and so on. 178 Upon measurement, the qubit loses its superposition and irreversibly 179 collapses into one of the two basis states, either |0> or |1>. Which 180 of the two states it ends up in may not be deterministic, but can be 181 determined from the readout of the measurement. The measurement 182 result is a classical bit, 0 or 1, corresponding to |0> and |1> 183 respectively. The probability of measuring the state in the |0> 184 state is |a|^2 and similarly the probability of measuring the state 185 in the |1> state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness 186 is not due to our ignorance of the underlying mechanisms, but rather 187 is a fundamental feature of a quantum mechanical system [9]. 189 The superposition property plays an important role in fundamental 190 gate operations on qubits. Since a qubit can exist in a 191 superposition of its basis states, the elementary quantum gates are 192 able to act on all states of the superposition at the same time. For 193 example, consider the NOT gate: 195 NOT (a |0> + b |1>) -> a |1> + b |0>. 197 2.2. Multiple qubits 199 When multiple qubits are combined in a single quantum state the space 200 of possible states grows exponentially and all these states can 201 coexist in a superposition. For example, the general form of a two- 202 qubit register is 204 a |00> + b |01> + c |10> + d |11> 206 where the coefficients have the same probability amplitude 207 interpretation as for the single qubit state. Each state represents 208 a possible outcome of a measurement of the two-qubit register. For 209 example, |01> denotes a state in which the first qubit is in the 210 state |0> and the second is in the state |1>. 212 Performing single qubit gates affects the relevant qubit in each of 213 the superposition states. Similarly, two-qubit gates also act on all 214 the relevant superposition states, but their outcome is far more 215 interesting. 217 Consider a two-qubit register where the first qubit is in the 218 superposed state (|0> + |1>)/sqrt(2) and the other is in the 219 state |0>. This combined state can be written as: 221 (|0> + |1>)/sqrt(2) x |0> = (|00> + |10>)/sqrt(2), 223 where x denotes a tensor product (the mathematical mechanism for 224 combining quantum states together). Let us now consider the two- 225 qubit controlled-NOT, or CNOT, gate. The CNOT gate takes as input 226 two qubits, a control and target, and applies the NOT gate to the 227 target if the control qubit is set. The truth table looks like 229 +----+-----+ 230 | IN | OUT | 231 +----+-----+ 232 | 00 | 00 | 233 | 01 | 01 | 234 | 10 | 11 | 235 | 11 | 10 | 236 +----+-----+ 238 Now, consider performing a CNOT gate on the state with the first 239 qubit being the control. We apply a two-qubit gate on all the 240 superposition states: 242 CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2). 244 What is so interesting about this two-qubit gate operation? The 245 final state is *entangled*. There is no possible way of representing 246 that quantum state as a product of two individual qubits; they are no 247 longer independent and the behaviour of either qubit cannot be fully 248 described without accounting for the other qubit. The states of the 249 two individual qubits are now correlated beyond what is possible to 250 achieve classically. Neither qubit is in a definite |0> or |1> 251 state, but if we perform a measurement on either one, the outcome of 252 the partner qubit will *always* yield the exact same outcome. The 253 final state, whether it's |00> or |11>, is fundamentally random as 254 before, but the states of the two qubits following a measurement will 255 always be identical. 257 Once a measurement is performed, the two qubits are once again 258 independent. The final state is either |00> or |11> and both of 259 these states can be trivially decomposed into a product of two 260 individual qubits. The entanglement has been consumed and the 261 entangled state must be prepared again. 263 3. Entanglement as the fundamental resource 265 Entanglement is the fundamental building block of quantum networks. 266 Consider the state from the previous section: 268 (|00> + |11>)/sqrt(2). 270 Neither of the two qubits is in a definite |0> or |1> state and we 271 need to know the state of the entire register to be able to fully 272 describe the behaviour of the two qubits. 274 Entangled qubits have interesting non-local properties. Consider 275 sending one of the qubits to another device. This device could in 276 principle be anywhere: on the other side of the room, in a different 277 country, or even on a different planet. Provided negligible noise 278 has been introduced, the two qubits will forever remain in the 279 entangled state until a measurement is performed. The physical 280 distance does not matter at all for entanglement. 282 This lies at the heart of quantum networking, because it is possible 283 to leverage the non-classical correlations provided by entanglement 284 in order to design completely new types of application protocols that 285 are not possible to achieve with just classical communication. 286 Examples of such applications are quantum cryptography [3] [4], blind 287 quantum computation [28], or distributed quantum computation [5]. 289 Entanglement has two very special features from which one can derive 290 some intuition about the types of applications enabled by a quantum 291 network. 293 The first stems from the fact that entanglement enables stronger than 294 classical correlations, leading to opportunities for tasks that 295 require coordination. As a trivial example, consider the problem of 296 consensus between two nodes who want to agree on the value of a 297 single bit. They can use the quantum network to prepare the state 298 (|00> + |11>)/sqrt(2) with each node holding one of the two qubits. 299 Once either of the two nodes performs a measurement, the state of the 300 two qubits collapses to either |00> or |11>, so whilst the outcome is 301 random and does not exist before measurement, the two nodes will 302 always measure the same value. We can also build the more general 303 multi-qubit state (|00...> + |11...>)/sqrt(2) and perform the same 304 algorithm between an arbitrary number of nodes. These stronger than 305 classical correlations generalise to more complicated measurement 306 schemes as well. 308 The second feature of entanglement is that it cannot be shared, in 309 the sense that if two qubits are maximally entangled with each other, 310 then it is physically impossible for any other system to have any 311 share of this entanglement [29]. Hence, entanglement forms a sort of 312 private and inherently untappable connection between two nodes once 313 established. 315 Entanglement is created through local interactions between two qubits 316 or as a product of the way the qubits were created (e.g. entangled 317 photon pairs). To create a distributed entangled state, one can then 318 physically send one of the qubits to a remote node. It is also 319 possible to directly entangle qubits that are physically separated, 320 but this still requires local interactions between some other qubits 321 that the separated qubits are initially entangled with. Therefore, 322 it is the transmission of qubits that draws the line between a 323 genuine quantum network and a collection of quantum computers 324 connected over a classical network. 326 A quantum network is defined as a collection of nodes that is able to 327 exchange qubits and distribute entangled states amongst themselves. 328 A quantum node that is able only to communicate classically with 329 another quantum node is not a member of a quantum network. 331 More complex services and applications can be built on top of 332 entangled states distributed by the network, see e.g. [35] 334 4. Achieving quantum connectivity 336 This section explains the meaning of quantum connectivity and the 337 necessary physical processes at an abstract level. 339 4.1. Challenges 341 A quantum network cannot be built by simply extrapolating all the 342 classical models to their quantum analogues. Sending qubits over a 343 wire like we send classical bits is simply not as easy to do. There 344 are several technological as well as fundamental challenges that make 345 classical approaches unsuitable in a quantum context. 347 4.1.1. The measurement problem 349 In classical computers and networks we can read out the bits stored 350 in memory at any time. This is helpful for a variety of purposes 351 such as copying, error detection and correction, and so on. This is 352 not possible with qubits. 354 A measurement of a qubit's state will destroy its superposition and 355 with it any entanglement it may have been part of. Once a qubit is 356 being processed, it cannot be read out until a suitable point in the 357 computation, determined by the protocol handling the qubit, has been 358 reached. Therefore, we cannot use the same methods known from 359 classical computing for the purposes of error detection and 360 correction. Nevertheless, quantum error detection and correction 361 schemes exist that take this problem into account and how a network 362 chooses to manage errors will have an impact on its architecture. 364 4.1.2. No-cloning theorem 366 Since directly reading the state of a qubit is not possible, one 367 could ask if we can simply copy a qubit without looking at it. 368 Unfortunately, this is fundamentally not possible in quantum 369 mechanics [30] [31]. 371 The no-cloning theorem states that it is impossible to create an 372 identical copy of an arbitrary, unknown quantum state. Therefore, it 373 is also impossible to use the same mechanisms that worked for 374 classical networks for signal amplification, retransmission, and so 375 on as they all rely on the ability to copy the underlying data. 376 Since any physical channel will always be lossy, connecting nodes 377 within a quantum network is a challenging endeavour and its 378 architecture must at its core address this very issue. 380 4.1.3. Fidelity 382 In general, it is expected that a classical packet arrives at its 383 destination without any errors introduced by hardware noise along the 384 way. This is verified at various levels through a variety of error 385 detection and correction mechanisms. Since we cannot read or copy a 386 quantum state error detection and correction is more involved. 388 To describe the quality of a quantum state, a physical quantity 389 called fidelity is used [16]. Fidelity takes a value between 0 and 1 390 -- higher is better, and less than 0.5 means the state is unusable. 391 It measures how close a quantum state is to the state we have tried 392 to create. It expresses the probability that one state will pass a 393 test to identify as the other. Fidelity is an important property of 394 a quantum system that allows us to quantify how much a particular 395 state has been affected by noise from various sources (gate errors, 396 channel losses, environment noise). 398 Interestingly, quantum applications do not need perfect fidelity to 399 be able to execute -- as long as the fidelity is above some 400 application-specific threshold, they will simply operate at lower 401 rates. Therefore, rather than trying to ensure that we always 402 deliver perfect states (a technologically challenging task) 403 applications will specify a minimum threshold for the fidelity and 404 the network will try its best to deliver it. A higher fidelity can 405 be achieved by either having hardware produce states of better 406 fidelity (sometimes one can sacrifice rate for higher fidelity) or by 407 employing quantum error detection and correction mechanisms. 409 4.1.4. Inadequacy of direct transmission 411 Conceptually, the most straightforward way to distribute an entangled 412 state is to simply transmit one of the qubits directly to the other 413 end across a series of nodes while performing sufficient forward 414 quantum error correction (Section 4.4.3.2) to bring losses down to an 415 acceptable level. Despite the no-cloning theorem and the inability 416 to directly measure a quantum state, error-correcting mechanisms for 417 quantum communication exist [33] [32] [38] [10]. However, quantum 418 error correction makes very high demands on both resources (physical 419 qubits needed) and their initial fidelity. Implementation is very 420 challenging and quantum error correction is not expected to be used 421 until later generations of quantum networks. 423 An alternative relies on the observation that we do not need to be 424 able to distribute any arbitrary entangled quantum state. We only 425 need to be able to distribute any one of what are known as the Bell 426 pair states [19]. 428 4.2. Bell pairs 430 Bell pair states are the entangled two-qubit states: 432 |00> + |11>, |00> - |11>, |01> + |10>, |01> - |10>, 434 where the constant 1/sqrt(2) normalisation factor has been ignored 435 for clarity. Any of the four Bell pair states above will do, as it 436 is possible to transform any Bell pair into another Bell pair with 437 local operations performed on only one of the qubits. When each 438 qubit in a Bell pair is held by a separate node, either node can 439 apply a series of single qubit gates to their qubit alone in order to 440 transform the state between the different variants. 442 Distributing a Bell pair between two nodes is much easier than 443 transmitting an arbitrary quantum state over a network. Since the 444 state is known, handling errors becomes easier and small-scale error- 445 correction (such as entanglement distillation discussed in a later 446 section) combined with reattempts becomes a valid strategy. 448 The reason for using Bell pairs specifically as opposed to any other 449 two-qubit state is that they are the maximally entangled two-qubit 450 set of basis states. Maximal entanglement means that these states 451 have the strongest non-classical correlations of all possible two- 452 qubit states. Furthermore, since single-qubit local operations can 453 never increase entanglement, less entangled states would impose some 454 constraints on distributed quantum algorithms. This makes Bell pairs 455 particularly useful as a generic building block for distributed 456 quantum applications. 458 4.3. Teleportation 460 The observation that we only need to be able to distribute Bell pairs 461 relies on the fact that this enables the distribution of any other 462 arbitrary entangled state. This can be achieved via quantum state 463 teleportation [18]. Quantum state teleportation consumes an unknown 464 qubit state that we want to transmit and recreates it at the desired 465 destination. This does not violate the no-cloning theorem as the 466 original state is destroyed in the process. 468 To achieve this, an entangled pair needs to be distributed between 469 the source and destination before teleportation commences. The 470 source then entangles the transmission qubit with its end of the pair 471 and performs a read out of the two qubits (the sum of these 472 operations is called a Bell state measurement). This consumes the 473 Bell pair's entanglement, turning the source and destination qubits 474 into independent states. The measurements yields two classical bits 475 which the source sends to the destination over a classical channel. 476 Based on the value of the received two classical bits, the 477 destination performs one of four possible corrections (called the 478 Pauli corrections) on its end of the pair, which turns it into the 479 unknown qubit state that we wanted to transmit. This requirement to 480 communicate the measurement read out over a classical channel 481 unfortunately means that entanglement cannot be used to transmit 482 information faster than the speed of light. 484 The unknown quantum state that was transmitted was never fed into the 485 network itself. Therefore, the network needs to only be able to 486 reliably produce Bell pairs between any two nodes in the network. 487 Thus, a key difference between a classical and quantum data planes is 488 that a classical one carries user data, but a quantum data plane 489 provides the resources for the user to transmit user data themselves 490 without further involvement of the network. 492 4.4. The life cycle of entanglement 494 Reducing the problem of quantum connectivity to one of generating a 495 Bell pair has facilitated the problem, but it has not solved it. In 496 this section, we discuss how these entangled pairs are generated in 497 the first place, and how their two qubits are delivered to the end- 498 points. 500 4.4.1. Elementary link generation 502 In a quantum network, entanglement is always first generated locally 503 (at a node or an auxiliary element) followed by a movement of one or 504 both of the entangled qubits across the link through quantum 505 channels. In this context, photons (particles of light) are the 506 natural candidate for entanglement carriers, called flying qubits. 507 The rationale for this choice is related to the advantages provided 508 by photons such as moderate interaction with the environment leading 509 to moderate decoherence, convenient control with standard optical 510 components, and high-speed, low-loss transmissions. However, since 511 photons cannot be stored, a transducer must transfer the flying 512 qubit's state to a qubit suitable for information processing and/or 513 storage (often referred to as a matter qubit). 515 Since this process may fail, in order to generate and store 516 entanglement efficiently, we must be able to distinguish successful 517 attempts from failures. Entanglement generation schemes that are 518 able to announce successful generation are called heralded 519 entanglement generation schemes. 521 There exist three basic schemes for heralded entanglement generation 522 on a link through coordinated action of the two nodes at the two ends 523 of the link [20]: 525 o "At mid-point": in this scheme an entangled photon pair source 526 sitting midway between the two nodes with matter qubits sends an 527 entangled photon through a quantum channel to each of the nodes. 528 There, transducers are invoked to transfer the entanglement from 529 the flying qubits to the matter qubits. In this scheme, the 530 transducers know if the transfers succeeded and are able to herald 531 successful entanglement generation via a message exchange over the 532 classical channel. 534 o "At source": in this scheme one of the two nodes sends a flying 535 qubit that is entangled with one of its matter qubits. A 536 transducer at the other end of the link will transfer the 537 entanglement from the flying qubit to one of its matter qubits. 538 Just like in the previous scheme, the transducer knows if its 539 transfer succeeded and is able to herald successful entanglement 540 generation with a classical message sent to the other node. 542 o "At both end-points": in this scheme both nodes send a flying 543 qubit that is entangled with one of their matter qubits. A 544 detector somewhere in between the nodes performs a joint 545 measurement on the two qubits, which stochastically projects the 546 remote matter qubits into an entangled quantum state. The 547 detector knows if the entanglement succeeded and is able to herald 548 successful entanglement generation by sending a message to each 549 node over the classical channel. 551 The "mid-point source" scheme is more robust to photon loss, but in 552 the other schemes the nodes retain greater control over the entangled 553 pair generation. 555 Note that whilst photons travel in a particular direction through the 556 quantum channel the resulting entangled pair of qubits does not have 557 a direction associated with it. Physically, there is no upstream or 558 downstream end of the pair. 560 4.4.2. Entanglement swapping 562 The problem with generating entangled pairs directly across a link is 563 that efficiency decreases with channel length. Beyond a few 10s of 564 kms in optical fibre or 1000 kms in free space (via satellite) the 565 rate is effectively zero and due to the no-cloning theorem we cannot 566 simply amplify the signal. The solution is entanglement swapping 567 [19]. 569 A Bell pair between any two nodes in the network can be constructed 570 by combining the pairs generated along each individual link on a path 571 between the two end-points. Each node along the path can consume the 572 two pairs on the two links that it is connected to in order to 573 produce a new entangled pair between the two remote ends. This 574 process is known as entanglement swapping. Pictorially it can be 575 represented as follows: 577 +---------+ +---------+ +---------+ 578 | A | | B | | C | 579 | |------| |------| | 580 | X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 | 581 +---------+ +---------+ +---------+ 583 where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2 584 are the qubits of entangled pair Y. The entanglement is denoted with 585 ~~. In the diagram above, nodes A and B share the pair X and nodes B 586 and C share the pair Y, but we want entanglement between A and C. 588 To achieve this goal, we simply teleport the qubit X2 using the pair 589 Y. This requires node B to perform a Bell state measurement on the 590 qubits X2 and Y1 which result in the destruction of the entanglement 591 between Y1 and Y2. However, X2 is recreated in Y2's place, carrying 592 with it its entanglement with X1. The end-result is shown below: 594 +---------+ +---------+ +---------+ 595 | A | | B | | C | 596 | |------| |------| | 597 | X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 | 598 +---------+ +---------+ +---------+ 600 Depending on the needs of the network and/or application, a final 601 Pauli correction at the recipient node may not be necessary since the 602 result of this operation is also a Bell pair. However, the two 603 classical bits that form the read out from the measurement at node B 604 must still be communicated, because they carry information about 605 which of the four Bell pairs was actually produced. If a correction 606 is not performed, the recipient must be informed which Bell pair was 607 received. 609 This process of teleporting Bell pairs using other entangled pairs is 610 called entanglement swapping. Quantum nodes that create long- 611 distance entangled pairs via entanglement swapping are called quantum 612 repeaters in academic literature [19] and we will use the same 613 terminology in this memo. 615 4.4.3. Error Management 617 4.4.3.1. Distillation 619 Neither the generation of Bell pairs nor the swapping operations are 620 noiseless operations. Therefore, with each link and each swap the 621 fidelity of the state degrades. However, it is possible to create 622 higher fidelity Bell pair states from two or more lower fidelity 623 pairs through a process called distillation (sometimes also referred 624 to as purification) [36]. 626 To distil a quantum state, a second (and sometimes third) quantum 627 state is used as a "test tool" to test a proposition about the first 628 state, e.g., "the parity of the two qubits in the first state is 629 even." When the test succeeds, confidence in the state is improved, 630 and thus the fidelity is improved. The test tool states are 631 destroyed in the process, so resource demands increase substantially 632 when distillation is used. When the test fails, the tested state 633 must also be discarded. Distillation makes low demands on fidelity 634 and resources compared to quantum error correction, but distributed 635 protocols incur round-trip delays due to classical communication 636 [17]. 638 4.4.3.2. Quantum Error Correction 640 Just like classical error correction, quantum error correction (QEC) 641 encodes logical qubits using several physical (raw) qubits to protect 642 them from errors described in Section 4.1.3 [33] [32] [38] [10]. 643 Furthermore, similarly to its classical counterpart, QEC can not only 644 correct state errors but also account for lost qubits. Additionally, 645 if all physical qubits which encode a logical qubit are located at 646 the same node, the correction procedure can be executed locally, even 647 if the logical qubit is entangled with remote qubits. 649 Although QEC was originally a scheme proposed to protect a qubit from 650 noise, QEC can also be applied to entanglement distillation. Such 651 QEC-applied distillation is cost-effective but requires a higher base 652 fidelity. 654 4.4.3.3. Error management schemes 656 Quantum networks have been categorized into three "generations" based 657 on the error management scheme they employ [10]. Note that these 658 "generations" are more like categories; they do not necessarily imply 659 a time progression and do not obsolete each other, though the later 660 generations do require more advanced technologies. Which generation 661 is used depends on the hardware platform and network design choices. 663 Table 1 summarises the generations. 665 +-----------+-----------------+------------------------+------------+ 666 | | First | Second generation | Third | 667 | | generation | | generation | 668 +-----------+-----------------+------------------------+------------+ 669 | Loss | Heralded | Heralded entanglement | Quantum | 670 | tolerance | entanglement | generation (bi- | Error | 671 | | generation (bi- | directional classical | Correction | 672 | | directional | signaling) | (no | 673 | | classical | | classical | 674 | | signaling) | | signaling) | 675 | | | | | 676 | Error | Entanglement | Entanglement | Quantum | 677 | tolerance | distillation | distillation (uni- | Error | 678 | | (bi-directional | directional classical | Correction | 679 | | classical | signaling) or | (no | 680 | | signaling) | Quantum Error | classical | 681 | | | Correction (no | signaling) | 682 | | | classical signaling) | | 683 +-----------+-----------------+------------------------+------------+ 685 Table 1: Classical signaling and generations 687 Generations are defined by the directions of classical signalling 688 required in their distributed protocols for loss tolerance and error 689 tolerance. Classical signalling carries the classical bits and 690 incurs round-trip delays described in Section 4.4.3.1, hence they 691 affect the performance of quantum networks, especially as the 692 distance between the communicating nodes increases. 694 Loss tolerance is about tolerating qubit transmission losses between 695 nodes. Heralded entanglement generation, as described in 696 Section 4.4.1, confirms the receipt of an entangled qubit using a 697 heralding signal. A pair of directly connected quantum nodes 698 repeatedly attempt to generate an entangled pair until the a 699 heralding signal is received. As described in Section 4.4.3.2, QEC 700 can be applied to complement lost qubits eliminating the need for re- 701 attempts. Furthermore, since the correction procedure is composed of 702 local operations, it does not require a heralding signal. However, 703 it is possible only when the photon loss rate from transmission to 704 measurement is less than 50%. 706 Error tolerance is about tolerating quantum state errors. 707 Entanglement distillation is the easiest mechanism for improved error 708 tolerance to implement, but it incurs round-trip delays due the 709 requirement for bi-directional classical signalling. The 710 alternative, QEC, is able to correct state errors locally so that it 711 does not need any classical signalling between the quantum nodes. In 712 between these two extremes, there is also QEC-applied distillation, 713 which requires uni-directional classical signalling. 715 The three "generations" summarised: 717 1. First generation quantum networks use heralding for loss 718 tolerance and entanglement distillation for error tolerance. 719 These networks can be implemented even with a limited set of 720 available quantum gates. 722 2. Second generation quantum networks improve upon the first 723 generation with QEC codes for error tolerance (but not loss 724 tolerance). At first, QEC will be applied to entanglement 725 distillation only which requires uni-directional classical 726 signalling. Later, QEC codes will be used to create logical Bell 727 pairs which no longer require any classical signalling for the 728 purposes of error tolerance. Heralding is still used to 729 compensate for transmission losses. 731 3. Third generation quantum networks directly transmit QEC encoded 732 qubits to adjacent nodes, as discussed in Section 4.1.4. 733 Elementary link Bell pairs can now be created without heralding 734 or any other classical signalling. Furthermore, this also 735 enables direct transmission architectures in which qubits are 736 forwarded end-to-end like classical packets rather than relying 737 on Bell pairs and entanglement swapping. 739 4.4.4. Delivery 741 Eventually, the Bell pairs must be delivered to an application (or 742 higher layer protocol) at the two end-nodes. A detailed list of such 743 requirements is beyond the scope of this memo. At minimum, the end- 744 nodes require information to map a particular Bell pair to the qubit 745 in their local memory that is part of this entangled pair. 747 5. Architecture of a quantum internet 749 It is evident from the previous sections that the fundamental service 750 provided by a quantum network significantly differs from that of a 751 classical network. Therefore, it is not surprising that the 752 architecture of a quantum internet will itself be very different from 753 that of the classical Internet. 755 5.1. Challenges 757 This subsection covers the major fundamental challenges building 758 quantum networks. Here, we only describe the fundamental 759 differences. Technological limitations are described later. 761 1. Bell pairs are not equivalent to payload carrying packets. 763 In most classical networks, including Ethernet, Internet Protocol 764 (IP), and Multi-Protocol Label Switching (MPLS) networks, user 765 data is grouped into packets. In addition to the user data, each 766 packet also contains a series of headers which contain the 767 control information that lets routers and switches forward it 768 towards its destination. Packets are the fundamental unit in a 769 classical network. 771 In a quantum network, the entangled pairs of qubits are the basic 772 unit of networking. These qubits themselves do not carry any 773 headers. Therefore, quantum networks will have to send all 774 control information via separate classical channels which the 775 repeaters will have to correlate with the qubits stored in their 776 memory. 778 2. "Store and forward" vs "store and swap" quantum networks. 780 As described in Section 4.4.1, quantum links provide Bell pairs 781 that are undirected network resources, in contrast to directed 782 frames of classical networks. This phenomenological distinction 783 leads to architectural differences between quantum networks and 784 classical networks. Quantum networks combine multiple elementary 785 link Bell pairs together to create one an end-to-end Bell pair, 786 whereas classical networks deliver messages from one end to the 787 other end hop by hop. 789 Classical networks receive data on one interface, store it in 790 local buffers, then forward the data to another appropriate 791 interface. Quantum networks store Bell pairs and then execute 792 entanglement swapping instead of forwarding in the data plane. 793 Such quantum networks are "store and swap" networks. In "store 794 and swap" networks, we do not need to care about the order in 795 which the Bell pairs were generated since they are undirected. 796 This distinction makes control algorithms and optimisation of 797 quantum networks different from classical ones. Note that third 798 generation quantum networks, as described in Section 4.4.1, will 799 be able to support a "store and forward" architecture in addition 800 to "store and swap". 802 3. An entangled pair is only useful if the locations of both qubits 803 are known. 805 A classical network packet logically exists only at one location 806 at any point in time. If a packet is modified in some way, 807 whether headers or payload, this information does not need to be 808 conveyed to anybody else in the network. The packet can be 809 simply forwarded as before. 811 In contrast, entanglement is a phenomenon in which two or more 812 qubits exist in a physically distributed state. Operations on 813 one of the qubits change the mutual state of the pair. Since the 814 owner of a particular qubit cannot just read out its state, it 815 must coordinate all its actions with the owner of the pair's 816 other qubit. Therefore, the owner of any qubit that is part of 817 an entangled pair must know the location of its counterpart. 818 Location, in this context, need not be the explicit spatial 819 location. A relevant pair identifier, a means of communication 820 between the pair owners, and an association between the pair ID 821 and the individual qubits is sufficient. 823 4. Generating entanglement requires temporary state. 825 Packet forwarding in a classical network is largely a stateless 826 operation. When a packet is received, the router does a lookup 827 in its forwarding table and sends the packet out of the 828 appropriate output. There is no need to keep any memory of the 829 packet any more. 831 A quantum node must be able to make decisions about qubits that 832 it receives and is holding in its memory. Since qubits do not 833 carry headers, the receipt of an entangled pair conveys no 834 control information based on which the repeater can make a 835 decision. The relevant control information will arrive 836 separately over a classical channel. This implies that a 837 repeater must store temporary state as the control information 838 and the qubit it pertains to will, in general, not arrive at the 839 same time. 841 5.2. Classical communication 843 In this memo we have already covered two different roles that 844 classical communication must perform: 846 o communicate classical bits of information as part of distributed 847 protocols such as entanglement swapping and teleportation, 849 o communicate control information within a network, including both 850 background protocols such as routing as well as signalling 851 protocols to set up end-to-end entanglement generation. 853 Classical communication is a crucial building block of any quantum 854 network. All nodes in a quantum network are assumed to have 855 classical connectivity with each other (within typical administrative 856 domain limts). Therefore, quantum routers will need to manage two 857 data planes in parallel, a classical one and a quantum one. 858 Additionally, a node must be able to correlate information between 859 the two planes so that the control information received on a 860 classical channel can be applied to the qubits managed by the quantum 861 data plane. 863 5.3. Abstract model of the network 865 5.3.1. The control and data planes 867 Control plane protocols for quantum networks will have many 868 responsibilities similar to their classical counterparts, namely 869 drawing the network topology, resource management, populating data 870 plane tables, etc. Most of these protocols do not require the 871 manipulation of quantum data and can operate simply by exchanging 872 classical messages only. There may also be some control plane 873 functionality that does require the handling of quantum data, e.g. a 874 quantum ping [2]. As it is not clear if there is much benefit in 875 defining a separate quantum control plane given the significant 876 overlap in responsibilities with its classical counterpart, the 877 question of whether there should be a separate quantum control plane 878 is beyond the scope of this document. 880 However, the data plane separation is much more distinct and there 881 will be two data planes: a classical data plane and a quantum data 882 plane. The classical data plane processes and forwards classical 883 packets. The quantum data plane processes and swaps entangled pairs. 884 Third generation quantum networks may also forward qubits in addition 885 to swapping Bell pairs. 887 In addition to control plane messages, there will also be control 888 information messages that operate at the granularity of individual 889 entangled pairs, such as heralding messages used for elementary link 890 generation (Section 4.4.1). In terms of functionality, these 891 messages are closer to classical packet headers than control plane 892 messages and thus we consider them to be part of the quantum data 893 plane. Therefore, a quantum data plane also includes the exchange of 894 classical control information at the granularity of individual qubits 895 and entangled pairs. 897 5.3.2. Elements of a quantum network 899 We have identified quantum repeaters as the core building block of a 900 quantum network. However, a quantum repeater will have to do more 901 than just entanglement swapping in a functional quantum network. Its 902 key responsibilities will include: 904 1. Creating link-local entanglement between neighbouring nodes. 906 2. Extending entanglement from link-local pairs to long-range pairs 907 through entanglement swapping. 909 3. Performing distillation to manage the fidelity of the produced 910 pairs. 912 4. Participating in the management of the network (routing, etc.). 914 Not all quantum repeaters in the network will be the same; here we 915 break them down further: 917 o Quantum routers (controllable quantum nodes) - A quantum router is 918 a quantum repeater with a control plane that participates in the 919 management of the network and will make decisions about which 920 qubits to swap to generate the requested end-to-end pairs. 922 o Automated quantum nodes - An automated quantum node is a data 923 plane only quantum repeater that does not participate in the 924 network control plane. Since the no-cloning theorem precludes the 925 use of amplification, long-range links will be established by 926 chaining multiple such automated nodes together. 928 o End-nodes - End-nodes in a quantum network must be able to receive 929 and handle an entangled pair, but they do not need to be able to 930 perform an entanglement swap (and thus are not necessarily quantum 931 repeaters). End-nodes are also not required to have any quantum 932 memory as certain quantum applications can be realised by having 933 the end-node measure its qubit as soon as it is received. 935 o Non-quantum nodes - Not all nodes in a quantum network need to 936 have a quantum data plane. A non-quantum node is any device that 937 can handle classical network traffic. 939 Additionally, we need to identify two kinds of links that will be 940 used in a quantum network: 942 o Quantum links - A quantum link is a link which can be used to 943 generate an entangled pair between two directly connected quantum 944 repeaters. This may include additional mid-point elements 945 described in Section 4.4.1. It may also include a dedicated 946 classical channel that is to be used solely for the purpose of 947 coordinating the entanglement generation on this quantum link. 949 o Classical links - A classical link is a link between any node in 950 the network that is capable of carrying classical network traffic. 952 Note that passive elements, such as optical switches, do not destroy 953 the quantum state. Therefore, it is possible to connect multiple 954 quantum nodes with each other over an optical network and perform 955 optical switching rather than routing via entanglement swapping at 956 quantum routers. This does require coordination with the elementary 957 link entanglement generation process and it still requires repeaters 958 to overcome the short-distance limitations. However, this is a 959 potentially feasible architecture for local area networks. 961 5.3.3. Putting it all together 963 A two-hop path in a generic quantum network can be represented as: 965 | App |-------------------CC-------------------| App | 966 || || 967 ------ ------ ------ 968 | EN |----QL & CC----| QR |----QL & CC----| EN | 969 ------ ------ ------ 971 App - user-level application 972 QR - quantum repeater 973 EN - end-node 974 QL - quantum link 975 CC - classical channel (can consist of many classical links) 977 An application running on two end-nodes attached to a network will at 978 some point need the network to generate entangled pairs for its use. 979 This may require negotiation between the end-nodes (possibly ahead of 980 time), because they must both open a communication end-point which 981 the network can use to identify the two ends of the connection. The 982 two end-nodes use the classical connectivity available in the network 983 to achieve this goal. 985 When the network receives a request to generate end-to-end entangled 986 pairs it uses the classical communication channels to coordinate and 987 claim the resources necessary to fulfill this request. This may be 988 some combination of prior control information (e.g. routing tables) 989 and signalling protocols, but the details of how this is achieved are 990 an active research question and thus beyond the scope of this memo. 992 During or after the distribution of control information, the network 993 performs the necessary quantum operations such as generating 994 entanglement over individual links, performing entanglement swaps, 995 and further signalling to transmit the swap outcomes and other 996 control information. Since Bell pairs do not carry any user data, 997 some of these operations can be performed before the request is 998 received in anticipation of the demand. 1000 The entangled pair is delivered to the application once it is ready, 1001 together with the relevant pair identifier. However, being ready 1002 does not necessarily mean that all link pairs and entanglement swaps 1003 are complete, as some applications can start executing on an 1004 incomplete pair. In this case the remaining entanglement swaps will 1005 propagate the actions across the network to the other end, sometimes 1006 necessitating fixup operations at the end node. 1008 5.4. Network boundaries 1010 Just like classical networks, various boundaries will exist in 1011 quantum networks. 1013 5.4.1. Boundaries between different physical architectures 1015 There are many different physical architectures for implementing 1016 quantum repeater technology. The different technologies differ in 1017 how they store and manipulate qubits in memory and how they generate 1018 entanglement across a link with their neighbours. Different 1019 architectures come with different trade-offs and thus a functional 1020 network will likely consist of a mixture of different types of 1021 quantum repeaters. 1023 For example, architectures based on optical elements and atomic 1024 ensembles [39] are very efficient at generating entanglement, but 1025 provide little control over the qubits once the pair is generated. 1026 On the other hand, nitrogen-vacancy architectures [27] offer a much 1027 greater degree of control over qubits, but have a harder time 1028 generating the entanglement across a link. 1030 It is an open research question where exactly the boundary will lie. 1031 It could be that a single quantum repeater node provides some 1032 backplane connection between the architectures, but it also could be 1033 that special quantum links delineate the boundary. 1035 5.4.2. Boundaries between different administrative regions 1037 Just like in classical networks, multiple quantum networks will 1038 connect into a global quantum internet. This necessarily implies the 1039 existence of borders between different administrative regions. How 1040 these boundaries will be handled is also an open question and thus 1041 beyond the scope of this memo. 1043 5.4.3. Boundaries between different error management schemes 1045 Not only are there physical differences and administrative 1046 boundaries, but there are important distinctions in how errors will 1047 be managed, as described in Section 4.4.3.3, which affect the content 1048 and semantics of messages that must cross those boundaries -- both 1049 for connection setup and real-time operation [42]. How to 1050 interconnect those schemes is also an open research question. 1052 5.5. Physical constraints 1054 The model above has effectively abstracted away the particulars of 1055 the hardware implementation. However, certain physical constraints 1056 need to be considered in order to build a practical network. Some of 1057 these are fundamental constraints and no matter how much the 1058 technology improves, they will always need to be addressed. Others 1059 are artefacts of the early stages of a new technology. Here, we 1060 consider a highly abstract scenario and refer to [8] for pointers to 1061 the physics literature. 1063 5.5.1. Memory lifetimes 1065 In addition to discrete operations being imperfect, storing a qubit 1066 in memory is also highly non-trivial. The main difficulty in 1067 achieving persistent storage is that it is extremely challenging to 1068 isolate a quantum system from the environment. The environment 1069 introduces an uncontrollable source of noise into the system which 1070 affects the fidelity of the state. This process is known as 1071 decoherence. Eventually, the state has to be discarded once its 1072 fidelity degrades too much. 1074 The memory lifetime depends on the particular physical setup, but the 1075 highest achievable values in quantum network hardware currently are 1076 on the order of seconds [40] although a lifetime of a minute has also 1077 been demonstrated for qubits not connected to a quantum network [41] 1078 (as of 2020). These values have increased tremendously over the 1079 lifetime of the different technologies and are bound to keep 1080 increasing. However, if quantum networks are to be realised in the 1081 near future, they need to be able to handle short memory lifetimes, 1082 for example by reducing latency on critical paths. 1084 5.5.2. Rates 1086 Entanglement generation on a link between two connected nodes is not 1087 a very efficient process and it requires many attempts to succeed 1088 [27] [14]. Currently, the highest achievable rates of success 1089 between nodes capable of storing the resulting qubits are on the 1090 order of 10 Hz. Combined with short memory lifetimes this leads to 1091 very tight timing windows to build up network-wide connectivity. 1093 5.5.3. Communication qubits 1095 Most physical architectures capable of storing qubits are only able 1096 to generate entanglement using only a subset of available qubits 1097 called communication qubits [14]. Once a Bell pair has been 1098 generated using a communication qubit, its state can be transferred 1099 into memory. This may impose additional limitations on the network. 1100 In particular, if a given node has only one communication qubit it 1101 cannot simultaneously generate Bell pairs over two links. It must 1102 generate entanglement over the links one at a time. 1104 5.5.4. Homogeneity 1106 Currently all hardware implementations are homogeneous and they do 1107 not interface with each other. In general, it is very challenging to 1108 combine different quantum information processing technologies at 1109 present. Coupling different technologies with each other is of great 1110 interest as it may help overcome the weaknesses of the different 1111 implementations, but this may take a long time to be realised with 1112 high reliability and thus is not a near-term goal. 1114 6. Architectural principles 1116 Given that the most practical way of realising quantum network 1117 connectivity is using Bell pair and entanglement swapping repeater 1118 technology, what sort of principles should guide us in assembling 1119 such networks such that they are functional, robust, efficient, and 1120 most importantly, they work? Furthermore, how do we design networks 1121 so that they work under the constraints imposed by the hardware 1122 available today, but do not impose unnecessary burdens on future 1123 technology? 1125 As quantum networking is a completely new technology that is likely 1126 to see many iterations over its lifetime, this memo must not serve as 1127 a definitive set of rules, but merely as a general set of recommended 1128 guidelines for the first generations of quantum networks based on 1129 principles and observations made by the community. The benefit of 1130 having a community built document at this early stage is that 1131 expertise in both quantum information and network architecture is 1132 needed in order to successfully build a quantum internet. 1134 6.1. Goals of a quantum internet 1136 When outlining any set of principles we must ask ourselves what goals 1137 do we want to achieve as inevitably trade-offs must be made. So what 1138 sort of goals should drive a quantum network architecture? The 1139 following list has been inspired by the history of computer 1140 networking and thus it is inevitably very similar to one that could 1141 be produced for the classical Internet [23]. However, whilst the 1142 goals may be similar the challenges involved are often fundamentally 1143 different. The list will also most likely evolve with time and the 1144 needs of its users. 1146 1. Support distributed quantum applications 1148 This goal seems trivially obvious, but makes a subtle, but 1149 important point which highlights a key difference between quantum 1150 and classical networks. Ultimately, quantum data transmission is 1151 not the goal of a quantum network - it is only one possible 1152 component of more advanced quantum application protocols [8]. 1153 Whilst transmission certainly could be used as a building block 1154 for all quantum applications, it is not the most basic one 1155 possible. For example, entanglement-based QKD, the most well 1156 known quantum application protocol, only relies on the stronger- 1157 than-classical correlations and inherent secrecy of entangled 1158 Bell pairs and does not have to transmit arbitrary quantum states 1159 [4]. 1161 The primary purpose of a quantum internet is to support 1162 distributed quantum application protocols and it is of utmost 1163 importance that they can run well and efficiently. Thus, it is 1164 important to develop performance metrics meaningful to 1165 application to drive the development of quantum network 1166 protocols. For example, the Bell pair generation rate is 1167 meaningless if one does not also consider their fidelity. It is 1168 generally much easier to generate pairs of lower fidelity, but 1169 quantum applications may have to make multiple re-attempts or 1170 even abort if the fidelity is too low. A review of the 1171 requirements for different known quantum applications can be 1172 found in [8] and an overview of use-cases can be found in [2]. 1174 2. Support tomorrow's distributed quantum applications 1176 The only principle of the Internet that should survive 1177 indefinitely is the principle of constant change [1]. Technical 1178 change is continuous and the size and capabilities of the quantum 1179 internet will change by orders of magnitude. Therefore, it is an 1180 explicit goal that a quantum internet architecture be able to 1181 embrace this change. We have the benefit of having been witness 1182 to the evolution of the classical Internet over several decades 1183 and seen what worked and what did not. It is vital for a quantum 1184 internet to avoid the need for flag days (e.g. NCP to TCP/IP) or 1185 upgrades that take decades to roll out (e.g. IPv4 to IPv6). 1187 Therefore, it is important that any proposed architecture for 1188 general purpose quantum repeater networks can integrate new 1189 devices and solutions as they become available. The architecture 1190 should not be constrained due to considerations for early-stage 1191 hardware and applications. For example, it is already possible 1192 to run QKD efficiently on metropolitan scales and such networks 1193 are already commercially available. However, they are not based 1194 on quantum repeaters and thus will not be able to easily 1195 transition to more sophisticated applications. 1197 3. Support heterogeneity 1199 There are multiple proposals for realising practical quantum 1200 repeater hardware and they all have their advantages and 1201 disadvantages. Some may offer higher Bell pair generation rates 1202 on individual links at the cost of more difficult entanglement 1203 swap operations. Other platforms may be good all around, but are 1204 more difficult to build. 1206 In addition to physical boundaries, there may be distinctions in 1207 how errors are managed (Section 4.4.3.3). These difference will 1208 affect the content and semantics of messages that cross these 1209 boundaries -- both for connection setup and real-time operation. 1211 The optimal network configuration will likely leverage the 1212 advantages of multiple platforms to optimise the provided 1213 service. Therefore, it is an explicit goal to incorporate varied 1214 hardware and technology support from the beginning. 1216 4. Ensure security at the network level 1218 The question of security in quantum networks is just as critical 1219 as it is in the classical Internet, especially since enhanced 1220 security offered by quantum entanglement is one of the key 1221 driving factors. 1223 It turns out that as long as the underlying implementation 1224 corresponds to (or sufficiently approximates) theoretical models 1225 of quantum cryptography, quantum cryptographic protocols do not 1226 need the network to provide any guarantees about the 1227 confidentiality or integrity of the transmitted qubits or the 1228 generated entanglement. Instead, applications, such as QKD, 1229 establish such guarantees in an end-to-end fashion using the 1230 classical network in conjunction with the quantum one. 1232 Nevertheless, whilst applications can ensure their own secure 1233 operation, network protocols themselves should be security aware 1234 in order to protect the network itself and limit disruption. 1235 Whilst the applications remain secure they are not necessarily 1236 operational or as efficient in the presence of an attacker. 1238 Security concerns in quantum networks are described in more 1239 detail in [13] [12]. 1241 5. Make them easy to monitor 1243 In order to manage, evaluate the performance of, or debug a 1244 network it is necessary to have the ability to monitor the 1245 network while ensuring there will be mechanisms in place to 1246 protect the confidentiality and integrity of the devices 1247 connected to it. Quantum networks bring new challenges in this 1248 area so it should be a goal of a quantum network architecture to 1249 make this task easy. 1251 The fundamental unit of quantum information, the qubit, cannot be 1252 actively monitored as any readout irreversibly destroys its 1253 contents. One of the implications of this fact is that measuring 1254 an individual pair's fidelity is impossible. Fidelity is 1255 meaningful only as a statistical quantity which requires the 1256 constant monitoring and the sacrifice of generated Bell pairs for 1257 tomography or other methods. 1259 Furthermore, given one end of an entangled pair, it is impossible 1260 to tell where the other qubit is without any additional classical 1261 metadata. It is impossible to extract this information from the 1262 qubits themselves. This implies that tracking entangled pairs 1263 necessitates some exchange of classical information. This 1264 information might include (i) a reference to the entangled pair 1265 that allows distributed applications to coordinate actions on 1266 qubits of the same pair, (ii) the two bits from each entanglement 1267 swap necessary to identify the final state of the Bell pair 1268 (Section 4.4.2). 1270 6. Ensure availability and resilience 1272 Any practical and usable network, classical or quantum, must be 1273 able to continue to operate despite losses and failures, and be 1274 robust to malicious actors trying to disable connectivity. What 1275 differs in quantum networks as compared to classical networks in 1276 this regard is that we now have two data planes and two types of 1277 channels to worry about: a quantum and a classical one. 1278 Therefore, availability and resilience will most likely require a 1279 more advanced treatment than they do in classical networks. 1281 6.2. The principles of a quantum internet 1283 The principles support the goals, but are not goals themselves. The 1284 goals define what we want to build and the principles provide a 1285 guideline in how we might achieve this. The goals will also be the 1286 foundation for defining any metric of success for a network 1287 architecture, whereas the principles in themselves do not distinguish 1288 between success and failure. For more information about design 1289 considerations for quantum networks see [11] [14]. 1291 1. Entanglement is the fundamental service 1293 The key service that a quantum network provides is the 1294 distribution of entanglement between the nodes in a network. All 1295 distributed quantum applications are built on top of this key 1296 resource. Bell pairs are the minimal entanglement building block 1297 that is sufficient to develop these applications. However, a 1298 quantum network may also distribute multipartite entangled states 1299 (entangled states of three or more qubits) [21] as this may be 1300 more efficient under certain circumstances. 1302 2. Bell Pairs are indistinguishable 1304 Any two Bell Pairs between the same two nodes are 1305 indistinguishable for the purposes of an application provided 1306 they both satisfy its required fidelity threshold. This 1307 observation is likely to be key in enabling a more optimal 1308 allocation of resources in a network, e.g. for the purposes of 1309 provisioning resources to meet application demand. However, the 1310 qubits that make up the pair themselves are not indistinguishable 1311 and the two nodes operating on a pair must coordinate to make 1312 sure they are operating on qubits that belong to the same Bell 1313 pair. 1315 3. Fidelity is part of the service 1317 In addition to being able to deliver Bell pairs to the 1318 communication end-points, the Bell Pairs must be of sufficient 1319 fidelity. Unlike in classical networks where errors are 1320 effectively eliminated before reaching the application, many 1321 quantum applications only need imperfect entanglement to 1322 function. However, quantum applications will generally have a 1323 threshold for Bell pair fidelity below which they are no longer 1324 able to operate. Different applications will have different 1325 requirements for what fidelity they can work with. It is the 1326 network's responsibility to balance the resource usage with 1327 respect to the applications' requirements. It may be that it is 1328 cheaper for the network to provide lower fidelity pairs that are 1329 just above the threshold required by the application than it is 1330 to guarantee high fidelity pairs to all applications regardless 1331 of their requirements. 1333 4. Time is an expensive resource 1334 Time is not the only resource that is in short supply (memory, 1335 and communication qubits are as well), but ultimately it is the 1336 lifetime of quantum memories that imposes some of the most 1337 difficult conditions for operating an extended network of quantum 1338 nodes. Current hardware has low rates of Bell pair generation, 1339 short memory lifetimes, and access to a limited number of 1340 communication qubits. All these factors combined mean that even 1341 a short waiting queue at some node could be enough for a Bell 1342 pair to decohere or result in an end-to-end pair below an 1343 application's fidelity threshold. Therefore, managing the idle 1344 time of qubits holding live quantum states should be done 1345 carefully. Ideally by minimising the idle time, but potentially 1346 also by moving the quantum state for temporary storage to a 1347 quantum memory with a longer lifetime. 1349 5. Be flexible with regards to capabilities and limitations 1351 This goal encompasses two important points. First, the 1352 architecture should be able to function under the physical 1353 constraints imposed by the current generation hardware. Near- 1354 future hardware will have low entanglement generation rates, 1355 quantum memories able to hold a handful of qubits at best, and 1356 decoherence rates that will render many generated pairs unusable. 1358 Second, the architecture should not make it difficult to run the 1359 network over any hardware that may come along in the future. The 1360 physical capabilities of repeaters will improve and redeploying a 1361 technology is extremely challenging. 1363 7. A thought experiment inspired by classical networks 1365 To conclude, we discuss a plausible quantum network architecture 1366 inspired by MPLS. This is not an architecture proposal, but rather a 1367 thought experiment to give the reader an idea of what components are 1368 necessary for a functional quantum network. We use classical MPLS as 1369 a basis as it is well known and understood in the networking 1370 community. 1372 Creating end-to-end Bell pairs between remote end-points is a 1373 stateful distributed task that requires a lot of a-priori 1374 coordination. Therefore, a connection-oriented approach seems the 1375 most natural for quantum networks. In connection-oriented quantum 1376 networks, when two quantum application end-points wish to start 1377 creating end-to-end Bell pairs, they must first create a quantum 1378 virtual circuit (QVC). As an analogy, in MPLS networks end-points 1379 must establish a label switched path (LSP) before exchanging traffic. 1380 Connection-oriented quantum networks may also support virtual 1381 circuits with multiple end-points for creating multipartite 1382 entanglement. As an analogy, MPLS networks have the concept of 1383 multi-point LSPs for multicast. 1385 When a quantum application creates a quantum virtual circuit, it can 1386 indicate quality of service (QoS) parameters such as the required 1387 capacity in end-to-end Bell pairs per second (BPPS) and the required 1388 fidelity of the Bell pairs. As an analogy, in MPLS networks 1389 applications specify the required bandwidth in bits per second (BPS) 1390 and other constraints when they create a new LSP. 1392 Quantum networks need a routing function to compute the optimal path 1393 (i.e. the best sequence of routers and links) for each new quantum 1394 virtual circuit. The routing function may be centralized or 1395 distributed. In the latter case, the quantum network needs a 1396 distributed routing protocol. As an analogy, classical networks use 1397 routing protocols such as open shortest path first (OSPF) and 1398 intermediate-system to intermediate system (IS-IS). However, note 1399 that the definition of "shortest-path"/"least-cost" may be different 1400 in a quantum network to account for its non-classical features, such 1401 as fidelity [22]. 1403 Given the very scarce availability of resources in early quantum 1404 networks, a traffic engineering function is likely to be beneficial. 1405 Without traffic engineering, quantum virtual circuits always use the 1406 shortest path. In this case, the quantum network cannot guarantee 1407 that each quantum end-point will get its Bell pairs at the required 1408 rate or fidelity. This is analogous to "best effort" service in 1409 classical networks. 1411 With traffic engineering, quantum virtual circuits choose a path that 1412 is guaranteed to have the requested resources (e.g. bandwidth in 1413 BPPS) available, taking into account the capacity of the routers and 1414 links and taking into account the resources already consumed by other 1415 virtual circuits. As an analogy, both OSPF and IS-IS have traffic 1416 engineering (TE) extensions to keep track of used and available 1417 resources, and can use constrained shortest path first (CSPF) to take 1418 resource availability and other constraints into account when 1419 computing the optimal path. 1421 The use of traffic engineering implies the use of call admission 1422 control (CAC): the network denies any virtual circuits for which it 1423 cannot guarantee the requested quality of service a-priori. Or 1424 alternatively, the network pre-empts lower priority circuits to make 1425 room for the new one. 1427 Quantum networks need a signaling function: once the path for a 1428 quantum virtual circuit has been computed, signaling is used to 1429 install the "forwarding rules" into the data plane of each quantum 1430 router on the path. The signaling may be distributed, analogous to 1431 the resource reservation protocol (RSVP) in MPLS. Or the signaling 1432 may be centralized, similar to OpenFlow. 1434 Quantum networks need an abstraction of the hardware for specifying 1435 the forwarding rules. This allows us to de-couple the control plane 1436 (routing and signaling) from the data plane (actual creation of Bell 1437 pairs). The forwarding rules are specified using abstract building 1438 blocks such as "creating local Bell pairs", "swapping Bell pairs", 1439 "distillation of Bell pairs". As an analogy, classical networks use 1440 abstractions that are based on match conditions (e.g. looking up 1441 header fields in tables) and actions (e.g. modifying fields or 1442 forwarding a packet to a specific interface). The data-plane 1443 abstractions in quantum networks will be very different from those in 1444 classical networks due to the fundamental differences in technology 1445 and the stateful nature of quantum networks. In fact, choosing the 1446 right abstractions will be one of the biggest challenges when 1447 designing interoperable quantum network protocols. 1449 In quantum networks, control plane traffic (routing and signaling 1450 messages) is exchanged over a classical channel, whereas data plane 1451 traffic (the actual Bell pair qubits) is exchanged over a separate 1452 quantum channel. This is in contrast to most classical networks, 1453 where control plane traffic and data plane traffic share the same 1454 channel and where a single packet contains both user fields and 1455 header fields. There is, however, a classical analogy to the way 1456 quantum networks work. Generalized MPLS (GMPLS) networks use 1457 separate channels for control plane traffic and data plane traffic. 1458 Furthermore, GMPLS networks support data planes where there is no 1459 such thing as data plane headers (e.g. DWDM or TDM networks). 1461 8. Security Considerations 1463 Security is listed as an explicit goal for the architecture and this 1464 issue is addressed in the section on goals. However, as this is an 1465 informational memo it does not propose any concrete mechanisms to 1466 achieve these goals. 1468 9. IANA Considerations 1470 This memo includes no request to IANA. 1472 10. Acknowledgements 1474 The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel 1475 Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang, 1476 Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG 1477 community as a whole for their very useful reviews and comments to 1478 the document. 1480 11. Informative References 1482 [1] Carpenter, B., Ed., "Architectural Principles of the 1483 Internet", RFC 1958, DOI 10.17487/RFC1958, June 1996, 1484 . 1486 [2] Wang, C., Rahman, A., Li, R., and M. Aelmans, 1487 "Applications and Use Cases for the Quantum Internet", 1488 draft-irtf-qirg-quantum-internet-use-cases-04 (work in 1489 progress), January 2021. 1491 [3] Bennett, C. and G. Brassard, "Quantum cryptography: Public 1492 key distribution and coin tossing", Theoretical Computer 1493 Science 560, 7-11, 2014, 1494 . 1496 [4] Ekert, A., "Quantum cryptography based on Bell's theorem", 1497 Phys. Rev. Lett. Vol. 67, Iss. 6, 1991, 1498 . 1501 [5] Crepeau, C., Gottesman, D., and A. Smith, "Secure multi- 1502 party quantum computation", Proceedings of Symposium on 1503 Theory of Computing , 2002, 1504 . 1506 [6] Giovanetti, V., Lloyd, S., and L. Maccone, "Quantum- 1507 enhanced measurements: beating the standard quantum 1508 limit", Science 306(5700), 1330-1336, 2004, 1509 . 1511 [7] Castelvecchi, D., "The Quantum Internet has arrived (and 1512 it hasn't)", Nature 554, 289-292, 2018, 1513 . 1515 [8] Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet: 1516 A vision for the road ahead", Science 362, 6412, 2018, 1517 . 1520 [9] Aspect, A., Grangier, P., and G. Roger, "Experimental 1521 tests of realistic local theories via Bell's theorem", 1522 Phys. Rev. Lett. 47 (7): 460-463, 1981, 1523 . 1526 [10] Muralidharan, S., Li, L., Kim, J., Lutkenhaus, N., Lukin, 1527 M., and L. Jiang, "Optimal architectures for long distance 1528 quantum communication", Nat. Sci. Rep. 6, 20463, 2016, 1529 . 1531 [11] Van Meter, R. and J. Touch, "Designing quantum repeater 1532 networks", IEEE Communications Magazine 51, 64-71, 2013, 1533 . 1535 [12] Satoh, T., Nagayama, S., Suzuki, S., Matsuo, T., and R. 1536 Van Meter, "Attacking the quantum internet", 1537 arXiv 2005.04617, 2020, 1538 . 1540 [13] Satoh, T., Nagayama, S., and R. Van Meter, "The network 1541 impact of hijacking a quantum repeater", Quantum Science 1542 and Technology Vol. 3, Iss. 3, 2017, 1543 . 1545 [14] Dahlberg, A., Skrzypczyk, M., Coopmans, T., Wubben, L., 1546 Rozpedek, F., Pompili, M., Stolk, A., Pawelczak, P., 1547 Knegjens, R., de Oliveira Filho, J., Hanson, R., and S. 1548 Wehner, "A link layer protocol for quantum networks", 1549 SIGCOMM '19 Proceedings of the ACM Special Interest Group 1550 on Data Communication 159-173, 2019, 1551 . 1553 [15] Sutor, R., "Dancing with Qubits", Packt Publishing , 2019. 1555 [16] Nielsen, M. and I. Chuang, "Quantum Computation and 1556 Quantum Information", Cambridge University Press , 2011. 1558 [17] Bennett, C., DiVincenzo, D., Smolin, J., and W. Wootters, 1559 "Mixed state entanglement and quantum error correction", 1560 Phys. Rev. A Vol. 54, Iss. 5, 1996, 1561 . 1563 [18] Bennett, C., Brassard, G., Crepeau, C., Jozsa, R., Peres, 1564 A., and W. Wootters, "Teleporting an unknown quantum state 1565 via dual classical and Einstein-Podolsky-Rosen channels", 1566 Phys. Rev. Lett. Vol. 70, Iss. 13, 1996, 1567 . 1570 [19] Briegel, H., Dur, W., Cirac, J., and P. Zoller, "Quantum 1571 repeaters: The role of imperfect local operations in 1572 quantum communication", Phys. Rev. Lett. Vol. 81, Num. 26, 1573 1998, . 1575 [20] Cacciapuoti, A., Caleffi, M., Van Meter, R., and L. Hanzo, 1576 "When Entanglement meets Classical Communications: Quantum 1577 Teleportation for the Quantum Internet", , 2019, 1578 . 1580 [21] Meignant, C., Markham, D., and F. Grosshans, "Distributing 1581 graph states over arbitrary quantum networks", Phys. Rev. 1582 A Vol. 100, Iss. 5, 2019, 1583 . 1585 [22] Van Meter, R., Satoh, T., Ladd, T., Munro, W., and K. 1586 Nemoto, "Path selection for quantum repeater networks", 1587 Networking Science Vol. 3, Iss. 1-4, pp 82-95, 2013, 1588 . 1590 [23] Clark, D., "The design philosophy of the DARPA internet 1591 protocols", SIGCOMM '88, 1988, 1592 . 1594 [24] Van Meter, R., "Quantum Networking", ISTE Ltd/John Wiley 1595 and Sons Inc 978-1-84821-537-5, 2014. 1597 [25] Aguado, A., Lopez, V., Diego, D., Peev, M., Poppe, A., 1598 Pastor, A., Folgueira, J., and M. Vicente, "The 1599 engineering of software-defined quantum key distribution 1600 networks", IEEE Communications Magazine Vol. 57, Iss. 7, 1601 2019, . 1603 [26] Peev, M., Pacher, C., Alleaume, R., Barreiro, C., Bouda, 1604 J., Boxleitner, W., Debuisschert, T., Diamanti, E., 1605 Dianati, M., Dynes, J., Fasel, S., Fossier, S., Fuerst, 1606 M., Gautier, J., Gay, O., Gisin, N., Grangier, P., Happe, 1607 A., Hasani, Y., Hentschel, M., Huebel, H., Humer, G., 1608 Laenger, T., Legre, M., Lieger, R., Lodewyck, J., 1609 Loruenser, T., Luetkenhaus, N., Marhold, A., Matyus, T., 1610 Maurhart, O., Monat, L., Nauerth, S., Page, J., Poppe, A., 1611 Querasser, E., Ribordy, G., Robyr, S., Salvail, L., 1612 Sharpe, A., Shields, A., Stucki, D., Suda, M., Tamas, C., 1613 Themel, T., Thew, R., Thoma, Y., Treiber, A., Trinkler, 1614 P., Tualle-Brouri, R., Vannel, F., Walenta, N., Weier, H., 1615 Weinfurter, H., Wimberger, I., Yuan, Z., Zbinden, H., and 1616 A. Zeilinger, "The SECOQC quantum key distribution network 1617 in Vienna", New J. Phys. Vol. 11, 2009, 1618 . 1620 [27] Hensen, B., Bernien, H., Dreau, A., Reiserer, A., Kalb, 1621 N., Blok, M., Ruitenberg, J., Vermeulen, R., Schouten, R., 1622 Abellan, C., Amaya, W., Pruneri, V., Mitchell, M., 1623 Markham, M., Twitchen, D., Elkouss, D., Wehner, S., 1624 Taminiau, T., and R. Hanson, "Loophole-free {Bell} 1625 inequality violation using electron spins separated by 1.3 1626 kilometres", Nature 526, 682-686, 2015, 1627 . 1629 [28] Fitzsimons, J. and E. Kashefi, "Unconditionally verifiable 1630 blind quantum computation", Phys. Rev. A Vol. 96, Iss. 1, 1631 2017, . 1633 [29] Terhal, B., "Is entanglement monogamous?", IBM Journal of 1634 Research and Development Vol. 48, Iss. 1, 2004, 1635 . 1637 [30] Park, J., "The concept of transition in quantum 1638 mechanics", Foundations of Physics Vol. 1, Iss. 1, 1970, 1639 . 1642 [31] Wootters, W. and W. Zurek, "A single quantum cannot be 1643 cloned", Nature 299, 802-803, 1982, 1644 . 1646 [32] Fowler, A., Wang, D., Hill, C., Ladd, T., Van Meter, R., 1647 and L. Hollenberg, "Surface code quantum communication", 1648 Phys. Rev. Lett. Vol. 104, Iss. 18, 2010, 1649 . 1651 [33] Jiang, L., Taylor, J., Nemoto, K., Munro, W., Van Meter, 1652 R., and M. Lukin, "Quantum repeater with encoding", Phys. 1653 Rev. A Vol. 79, Iss. 3, 2009, 1654 . 1656 [34] Gottesman, D., Jennewein, T., and S. Croke, "Longer- 1657 baseline telescopes using quantum repeaters", Phys. Rev. 1658 Lett. Vol. 109, Iss. 7, 2012, 1659 . 1661 [35] "The Quantum Protocol Zoo", . 1663 [36] Duer, W. and H. Briegel, "Entanglement purification and 1664 quantum error correction", Rep. Prog. Phys. Vol. 70, Iss. 1665 8, 2007, . 1667 [37] Kimble, H., "The Quantum Internet", Nature 453, 1023-1030, 1668 2008, . 1670 [38] Devitt, S., Nemoto, K., and W. Munro, "Quantum error 1671 correction for beginners", Rep. Prog. Phys. Vol. 76, Iss. 1672 7, 2013, . 1674 [39] Sangouard, N., Simon, C., de Riedmatten, H., and N. Gisin, 1675 "Quantum repeaters based on atomic ensembles and linear 1676 optics", Rev. Mod. Phys. Vol. 83, Iss. 1, 2011, 1677 . 1679 [40] Abobeih, M., Cramer, J., Bakker, M., Kalb, N., Markham, 1680 M., Twitchen, D., and T. Taminiau, "One-second coherence 1681 for a single electron spin coupled to a multi-qubit 1682 nuclear-spin environment", Nat. Comm. 9, 2552, 2018, 1683 . 1685 [41] Bradley, C., Randall, J., Abobeih, M., Berrevoets, R., 1686 Degen, M., Bakker, M., Markham, M., Twitchen, D., and T. 1687 Taminiau, "A 10-qubit solid-state spin register with 1688 quantum memory up to one minute", Phys. Rev. X Vol. 9, 1689 Iss. 3, 2019, . 1691 [42] Nagayama, S., Choi, B., Devitt, S., Suzuki, S., and R. Van 1692 Meter, "Interoperability in encoded quantum repeater 1693 networks", Phys. Rev. A Vol. 93, Iss. 4, 2016, 1694 . 1696 Authors' Addresses 1698 Wojciech Kozlowski 1699 QuTech 1700 Building 22 1701 Lorentzweg 1 1702 Delft 2628 CJ 1703 Netherlands 1705 Email: w.kozlowski@tudelft.nl 1706 Stephanie Wehner 1707 QuTech 1708 Building 22 1709 Lorentzweg 1 1710 Delft 2628 CJ 1711 Netherlands 1713 Email: s.d.c.wehner@tudelft.nl 1715 Rodney Van Meter 1716 Keio University 1717 5322 Endo 1718 Fujisawa, Kanagawa 252-0882 1719 Japan 1721 Email: rdv@sfc.wide.ad.jp 1723 Bruno Rijsman 1724 Individual 1726 Email: brunorijsman@gmail.com 1728 Angela Sara Cacciapuoti 1729 University of Naples Federico II 1730 Department of Electrical Engineering and Information Technologies 1731 Claudio 21 1732 Naples 80125 1733 Italy 1735 Email: angelasara.cacciapuoti@unina.it 1737 Marcello Caleffi 1738 University of Naples Federico II 1739 Department of Electrical Engineering and Information Technologies 1740 Claudio 21 1741 Naples 80125 1742 Italy 1744 Email: marcello.caleffi@unina.it 1745 Shota Nagayama 1746 Mercari, Inc. 1747 Roppongi Hills Mori Tower 18F 1748 6-10-1 Roppongi, Minato-ku 1749 Tokyo 106-6118 1750 Japan 1752 Email: shota.nagayama@mercari.com