Quantum Internet: Challenges and Opportunities Antônio J

Quantum Internet: Challenges and opportunities Antônio J. G. Abelém1, Gayane Vardoyan2, and Don Towsley2 1-Universidade Federal do Pará - UFPA 2-University of Massachuses - UMass, Amherst Introduction and Overview

Quantum Informaon and Quantum Compung Quantum Communication and Quantum Outline Networks Current Scenario and Challenges

Concluding Remarks

2 • The main motivation for a quantum Internet is to enable applications that are out of reach for the classical Internet. • Enhance Internet technology by quantum Introducon communication between any two points; • May operate in parallel to the classical internet • connecting quantum processors in order to achieve capabilities that are probably impossible by using only classical means.

3 RESEARCH

(Fig. 1) that bring advantages that are unattain- ture that makes qubits naturally well suited for rely solely on inherently quantum properties on October 16, 2019 • able with a classical network. Such applications security applications but at the same time makes such as quantum entanglement, which can be The best-known application of a quantum Internet is Quantum Key exploited already with very few qubits. By con- Distribution (QKD); Why Quantum Interet? trast, a quantum computer must feature more Fig. 1. Applications of a quantum Source: Physics World qubits than can be simulated on a classical com- internet. One application of a quan- puter in order to offer a computational advantage. • Other applications include: tum internet is to allow secure Given the challenges posed by the development of cryptography,access security to remote quantum– quantum com- key aquantuminternet,itisusefultoreflectonwhat • Secure communication: puters in the cloud (2). Specifically, a capabilities are needed to achieve specific quan- distribution (QKD)simple quantum terminal capable of tum applications and what technology is required • Secure access to remote quantum computerspreparing (in and measuringthe cloud) only single to realize them. (distributed) qubitsquantum can use a quantumcomputing internet to – Shor’s Here, we propose stages of development • Distributed quantum computing access a remote quantum computer toward a full-blown quantum internet. These algorithm, …in such a way that the quantum stages are functionality driven: Central to their • Quantum computing clusters; computer can learn nothing about definition is not the difficulty of experimentally which computation it has performed. achieving them but rather the essential question • high resolutionAlmost sensing all other applications of a quantum internet can be understood from two special features of of what level of complexity is needed to actually Tasks that require coordination: quantum entanglement. First, if two qubits at different network nodes are entangled with each enable useful applications. Each stage is inter- • clock synchronization, leader election, achievingother, then such consensus entanglement enables about stronger data, than classical Source:to helpIQOQI, correlation H. Ritsch two and coordination. For esting in its own right and distinguished by a high-precisionexample, clock for any synchronization measurement on qubit 1, if we made the same measurement on qubit 2, then we specific quantum functionality that is sufficient online bridge players coordinate their actions.instantaneously obtain the same answer, even though that answer is random and was not to support a certain class of protocols. To illus- determined ahead of time. Very roughly, it is this feature that makes entanglement so well suited for trate this, for each stage we give examples of • Scientific applications tasks that require coordination. Examples include clock synchronization (3), leader election, and known application protocols in which a quantum Source: MIT Technology achieving consensus about data (53), or even usingSource: entanglement nature.com to help two online bridge players internet is already known to bring advantages. coordinate their actions (39). The second feature of quantum entanglement is that it cannot be • such as combining light from distant telescopes to improve observations. 1 shared. If two qubits are maximally entangled with each other, then it is impossible by the4 laws of QuTech, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands. 2Kavli Institute of quantum mechanics for a third qubit to be just as entangled with either of them. This makes Nanoscience, Delft University of Technology, Post Office Box entanglement inherently private, bringing great advantages to tasks that require security such as 5046, 2600 GA Delft, Netherlands. generating encryption keys (12) or secure identification (24, 25). *Corresponding author. Email: [email protected]

Wehner et al., Science 362, eaam9288 (2018) 19 October 2018 1 of 9 QuantumElementary Information quantum and Quantum 101 Computing

bit has only two values: 0,1 • physicallyQuantum bit: represented qubit by two state device • Classical bit has only two values: 0,1 • physically represented by two state device

5 Quantum Information and Quantum Computing Quantum bits

• QuantumQuantumqubit -bits: two-state qubits bits quantum-mechanical system • The analogue of the classical bit is the quantum bit, or qubit for short. • example: photon polarization Likequbit a classical - two-state bit, aquantum-mechanical qubit has a state, system example: photon polarization

HorizontallyHorizontally polarized polarized VerticallyVertically polarized polarized 1 0 |�|0⟩⟩ 1 |�|1⟩ 0 |�⟩ 0 |�⟩ 1 • But... 0 1 6 Quantum bits 13

1.2 Quantum bits

The bit is the fundamental concept of classical computation and classical information. Quantum computation and quantum information are built upon an analogous concept, the quantum bit,orqubit for short. In this section we introduce the properties of single and multiple qubits, comparing and contrasting their properties to those of classical bits. What is a qubit? We’re going to describe qubits as mathematical objects with certain specific properties. ‘But hang on’, you say, ‘I thought qubits were physical objects.’ It’s true that qubits, like bits, are realized as actual physical systems, and in Section 1.5 and Chapter 7 we describe in detail how this connection between the abstract mathematical point of view and real systems is made. However, for the most part we treat qubits as abstract mathematical objects. The beauty of treating qubits as abstract entities is that it gives us the freedom to construct a general theory of quantum computation and quantum information which does not depend upon a specific system for its realization. Quantum InformationA classical bit mayand be examined manyQuantum times to determine whether it is in the stateComputing 0 or 1. However, a qubit generally cannot be examined to determine its full quantum state, that is, the values of a and b. Instead, quantum mechanics tells us that we can only What then is a qubit? Just as a classical bit hasacquire a muchstate more restricted information–either0or1–aqubitalso about the quantum state through a measurement operation. When we measure a qubit we get either the result 0, with probability a 2, or | | the result 1, with probability b 2. Naturally, a 2 + b 2 = 1, since the probabilities must | | | | | | has a state. Two possible states for a qubit are thesum states to one. Geometrically,0 we canand interpret this1 as the,whichasyoumight condition that the qubit’s state be normalized to length| 1.⟩ Thus, in general| a qubit’s⟩ state is a unit vector in a two- guess correspond to the states• Quantum 0 and bits: 1 for superposition a classicaldimensional complex bit. states vector Notation space. like ‘ ’iscalledthe As a 2 + b 2 = 1, y can also be expressed as: | | | | | i • classical bit is like a coin q q | ⟩ y = cos 0 + eij sin 1 . (9) Dirac notation,andwe’llbeseeingitoften,asit’sthestandardnotationforstatesin| i 2 | i 2 | i This equation facilitates the representation of a qubit’s state in a three-dimensional sphere, called Bloch sphere, as shown in Figure 2.1. The numbers q and j define a point on the quantum mechanics. The difference between bitsunit three-dimensional and qubits sphere. The south-north is that axis is the Z-axis, a qubit the positive X-axis can is be in a toward the reader (out of the page or screen) and the Y-axis is right-left. state other than 0 or 1 .Itisalsopossibletoform• qubit can exist in a continuumlinear of states combinations between|0〉andof |1 states,〉… often | ⟩ | ⟩ called superpositions: • until it is observed. Superposition of states ψ = α 0 + β 1 . (1.1) | ⟩ | ⟩ | ⟩ The numbers α�⟩and��β⟩ �|�are complex⟩, � numbers,� 1 although for many purposes not much is lost by thinking of them as real numbers. Put another way, the state of a qubit is a vector 8 Bloch sphere in a two-dimensional complex vector space. The special statesFigure 2.1. Bloch0 sphereand 1 are known as The Bloch sphere provides a useful means| ⟩ of visualizing the state| of⟩ a single qubit, and often serves as an excellent testbed for ideas about quantum computation and quantum computational basis states,andformanorthonormalbasisforthisvectorspace.information. If the vector points at the north pole, our qubit is in the 0 state, and if | i it points at the south pole, the qubit is in the 1 state. When the unit vector points | i toward you, that is the ( 0 + 1 )/p2 state; when it points away from you, that is the | i | i We can examine a bit to determine whether( it0 1 is)/p2 instate. These the two states state are called the 0+ and or(read 1. "ket For plus" and example, | i| i | i |i "ket minus") states. The positive Y-axis is ( 0 + i 1 )/p2 and the negative Y-axis is | i | i ( 0 i 1 )/p2. The phase is the position of the vector about the Z-axis. computers do this all the time when they retrieve| i the| i contents of their memory. Rather remarkably, we cannot examine a qubit to determine its quantum state, that is, the values of α and β.Instead,quantummechanicstellsusthatwecanonlyacquiremuch more restricted information about the quantum state. When we measure a qubit we get either the result 0, with probability α 2,ortheresult1,withprobability β 2.Naturally, | | | | α 2 + β 2 =1,sincetheprobabilitiesmustsumtoone.Geometrically,wecaninterpret |this| as| the| condition that the qubit’s state be normalized to length 1. Thus, in general a qubit’s state is a unit vector in a two-dimensional complex vector space. This dichotomy between the unobservable state of a qubit and the observations we can make lies at the heart of quantum computation and quantum information. In most of our abstract models of the world, there is a direct correspondence between elements of the abstraction and the real world, just as an architect’s plans for a building are in correspondence with the final building. The lack of this direct correspondence in quantum mechanics makes it difficult to intuit the behavior of quantum systems; however, there is an indirect correspondence, for qubit states can be manipulated and transformed in ways which lead to measurement outcomes which depend distinctly on the different properties of the state. Thus, these quantum states have real, experimentally verifiable consequences, which we shall see are essential to the power of quantum computation and quantum information. Quantum Informaon and Quantum Compung Two qubits Multiple qubits: Two qubits • Four four Basis basis states: states, 00⟩,01⟩,|10⟩,|11⟩ Two qubits

⟩ ⟩ ⟩ ⟩ ⟩ • A pair� fourof� qubits basis 00 states, can� also 0001⟩ ,01be� ⟩in,|10 superpositions10⟩,|11�⟩ |11 ,� of these 1four states:

�⟩ � 00⟩ � 01⟩ � 10⟩ � |11⟩,� 1 Bell state (Einstein-Podolsky-Rosen(EPR) pair)

|00⟩ |11⟩ Bell state (Einstein-Podolsky-Rosen(EPR) pair) 2 9 |00⟩ |11⟩ 2 Two qubits

four basis states, 00⟩,01⟩,|10⟩,|11⟩

�⟩ � 00⟩ � 01⟩ � 10⟩ �|11⟩,� 1 Quantum Informaon and Quantum Compung

BellMultiple state qubits:(Einstein-Podolsky-Rosen(EPR) Two qubits pair) • Bell state or Einstein-Podolsky-Rosen (EPR) pair: |00⟩ |11⟩ 2 • Bell pairs have the property that the qubits are correlated or entangled • Basis of quantum computing • Key ingredient in quantum teleportation and quantum networking.

10 Quantum is different

Quantum Information and Quantum Computing

Multiple qubits: Two qubits • Quantum entanglement is a quantumNo mechanical copying! phenomenon in which Short the lifetimes, quantum difficult states to of two or more objects have to be described manipulatewith reference many to qubits each other, even though the individual objects may be spatially separated.

Entanglement works differently - Inherently connected!

11 state. The ﬁdelity is 1.0 for a pure state and declines as noise in the system degrades the quality of the state. Consider, for example, we are initializing a two-qubit register to the y = 00 state, but that the initialization process is imperfect. To learn how imperfect, we | i repeat the process a number of times and measure the state, to build up a statistical picture of our ability to create the desired state. From this process, we obtain the density matrix ry and, then, we can calculate the ﬁdelity Fy for our desired state. For an n-qubit state, n the completely mixed state in which all qubits are random, we have F = 2 .

2.2.7. Bell pairs and GHZ states As we mentioned in Section 2.2.3, the best known two qubit entanglement involving two parts sharing two qubits is the Bell state. In the addition to the one listed in (11) there are three others forms of Bell pairs:

( 00 11 )/p2 (16) | i| i state. The( fidelity01 + 10 is)/ 1.0p2 for a pure state and declines (17) as noise in the system degrades the | i | i quality of the state. Consider, for example, we are initializing a two-qubit register to the ( 01 10 )/p2 (18) y = 00 state,| i but| i that the initialization process is imperfect. To learn how imperfect, we | i With Bell pairs (repeat11) and the(16 process), a measurement a number of of one times qubit and will measure result in the both state, to build up a statistical picture qubits being zero or bothof qubits our ability being one, to create with equal the desired probability. state. For From example, this Alice process, we obtain the density matrix may hold one qubit, whilery Boband, holds then, another we can one, calculate at an arbitrary the fidelity distanceF aparty for without our desired state. For an n-qubit state, the behavior of the Bell pair changing. When Alice measures her qubit and finds a one, n the completely mixed state in which all qubits are random, we have F = 2 . she will be sure that when Bob measures his qubit, it will be a one. Likewise, if she measures zero, Bob will2.2.7. measure Bell zero. pairs In (17 and) and GHZ(18), states in contrast, if Alice measures a one, Bob will measure a zero and vice-versa. Moreover, this effect does not change if BobQuantum measures his qubit Information firstAs or we if mentioned they both measure in Section their qubits 2.2.3, simultaneously. the best known two qubit entanglement involving two Other Bell States: andThere Quantum are other, largerparts Computing sharing multi-party two entangled qubits is states the Bell that state.are useful In the for addition a variety to the one listed in (11) there are of tasks, the Greenberger-Horne-Zeilingerthree others forms (GHZ) of Bell state pairs: [Bravyi et al. 2006]. It was first studied by Daniel Greenberger, Michael Horne and Anton Zeilinger in 1989. It involves at leastMultiple three subsystems qubits: (particleTwo qubits states, or qubits) and allows to observe extremely non- ( 00 11 )/p2 (16) classical properties of the state [Greenberger et al. 2007]. | i| i The GHZ state is an entangled quantum state of M > 2 subsystems.( 01 + 10 In)/p simple2 (17) words,• There it isare a other, quantum larger superposition of all subsystems being in state| i 0 or| alli of them multi-party entangled being in state 1, represented by: ( 01 10 )/p2 (18) states that are useful for | i| i a variety of tasks: • Greenberger-Horne- With000... Bell+ pairs111... (11) and (16), a measurement of one qubit will result in both Zeilinger (GHZ) state | i | i (19) qubits being zerop2 or both qubits being one, with equal probability. For example, Alice may hold one qubit, while Bob holds another one, at an arbitrary distance apart without There is no standardthe measure behavior of ofmulti-partite the Bell pairentanglement changing. because When different, Alice measuresnot her qubit and finds a one, mutually convertible, types of multi-partite entanglement exist. Nonetheless, many measures define the GHZ stateshe to bewill maximally be sure entangled that when state. Bob measures his qubit, it will be a one. Likewise, if she measures zero, Bob will measure zero. In (17) and (18),12 in contrast, if Alice measures GHZ states are useda one, in several Bob protocolswill measure in quantum a zero communication and vice-versa. and cryptog-Moreover, this effect does not change if raphy, including any of several common forms of three-party or larger states, for example, Bob measures his qubit first or if they both measure their qubits simultaneously. in secret sharing or in the Quantum Byzantine Agreement [Van Meter 2014]. There are other, larger multi-party entangled states that are useful for a variety of tasks, the Greenberger-Horne-Zeilinger (GHZ) state [Bravyi et al. 2006]. It was first studied by Daniel Greenberger, Michael Horne and Anton Zeilinger in 1989. It involves at least three subsystems (particle states, or qubits) and allows to observe extremely non- classical properties of the state [Greenberger et al. 2007]. The GHZ state is an entangled quantum state of M > 2 subsystems. In simple words, it is a quantum superposition of all subsystems being in state 0 or all of them being in state 1, represented by:

000... + 111... | i | i (19) p2

There is no standard measure of multi-partite entanglement because different, not mutually convertible, types of multi-partite entanglement exist. Nonetheless, many measures deﬁne the GHZ state to be maximally entangled state. GHZ states are used in several protocols in quantum communication and cryptography, including any of several common forms of three-party or larger states, for example, in secret sharing or in the Quantum Byzantine Agreement [Van Meter 2014]. Quantum Information and Quantum Computing

Measurement • In quantum physics, measurement is the testing or manipulation of a physical system in order to yield a numerical result. • The predictions that quantum physics makes are in general probabilistic. • When a qubit is measured, it only ever gives ʹ0ʹ or ʹ1ʹ as the measurement result – probabilistically.

Figure 2.6. symbol for measurement.

2.2.6. Interference, decoherence and fidelity In physics, interference is the combination of two or more waveforms to form a resultant wave, in which the displacement is either reinforced or canceled [Steel 1986]. Quantum interference can happen between particles that arrive at the same position or quantum state but by different paths. Quantum interference, a byproduct of superposition, is what allows us to bias the measurement of a qubit toward a desired state or set of states. Decoherence is the gradual decay of the state of a system. It happens because quantum states are very fragile: excited atoms decay and spins of electrons and atomic nuclei spontaneously flip. Any quantum system is affected through interactions with its environment, leaking information about its state out into the environment where it cannot be recovered. When decoherence occurs, measurement of the system may not produce the desired results, causing the failure of our quantum algorithm. The two key measures of decoherence are the T1 and T2 times. T1 is the energy relaxation time, and T2 is the phase relaxation time. Both processes are memoryless, with probabilistic behavior. The amount of time we can count on the state of a qubit remaining in a usable state is a function of the minimum of T1 and T2. Researchers determine these values experimentally, and an important area of device research is extending these times by careful engineering of the environment and control system. Fidelity is used to track the quality of the state. Fidelity ranges from 0 to 1.0, with the latter being perfect. It is, essentially, the probability that our qubit or set of qubits is actually in the state we believe it ought to be in. In other words, fidelity of a state corre- sponds to how imperfect it is in relation to a desired state [Jozsa 1994, Liang et al. 2019]. It is not a metric, but has some useful properties and it can be used to define a metric on this space of density matrices. We will define the fidelity as

F = y r y (15) h | | i where 0 F 1 is the ﬁdelity 2, y is the state we think we have created and r is the   | i density matrix of the actual state. The ﬁdelity can also be thought of the overlap of our actual state with the desired

2In literature, the fidelity is often defined as F = y r y , but in keeping with Jozsa’s definition h | | i [Jozsa 1994], adopted also in Van Meter’s book [Van Meter 2014], we dispense with the square root. p Quantum Informaon and Quantum Compung Measurement Measurement

uncountable number of states uncountable number of states Measurement • Single photon: • either � or � goes off, not both

• Repeat many times: single photon: either � or � goes off, not both Superposition of states repeat many times: �� single, �� photon: � either � or � goes off, not both repeat many times: �� , �� ⟩ ��⟩ �|�⟩, � � 1

14 Two qubits

four basis states, 00⟩,01⟩,|10⟩,|11⟩

�⟩ � 00⟩ � 01⟩ � 10⟩ �|11⟩,� 1 Quantum Informaon and Quantum Compung Bell state (Einstein-Podolsky-Rosen(EPR) pair) Measurement example: • Consider Bell state (EPR pair): |00⟩ |11⟩ 2 • measuring first qubit yields 0 or 1

• if 1, measuring second qubit yields 1

• if 0, measuring second qubit yields 0

15 Quantum Information and Quantum Computing

Imperfect quantum systems: • The state of a quantum system is exceedingly fragile. • Errors result in continuous degradation of our knowledge about the state of the quantum system. • Monitoring the system becomes extremely important. • As well as the management of error.

16 Quantum communication • Consists of either the exchange of quantum information or the sharing of Quantum entangled quantum state between two or more parties. Communication and Quantum Networks

17 Essential components • To transport qubits from one node to another, we need: Quantum • Quantum communication channels • Quantum repeaters (2 connections) or Communication routers or switches ( >3 connections) • End Nodes and Quantum What is a quantum network?

End Networks Node End Node Bridge long distances

End Repeater Node End Repeater Node

Prepare/Measure Qubits Store/Manipulate Qubits End Fiber Node (telecom) 18 Quantum channels • For the purpose of quantum communicaon channels, can be used: Quantum • Standard telecom ﬁbers • Free space. Communication Quantum communication – state of the art in space and Quantum Networks

Entanglement over a distance of > 1200km via satellite Pan Group, Science, July 2017

Yin et al. 2017. Satellite-based entanglement distribution over 1200 kilometers. Science 356, 6343 (jun 2017), 1140–1144 Sending Qubits via Entanglement Sending Qubits via Entanglement: Quantum Communication and Quantum Networks Sender Receiver

20 Sending Qubits via Entanglement Sending Qubits via Entanglement: Quantum Communication and Quantum Networks Sender Receiver

21 Sending Qubits via Entanglement Sending Qubits via Entanglement: Quantum Communicaon and Quantum Networks Sender Receiver

• Consumes the entanglement • Requires 2 bits of forward communication to the receiver. • Consumes the entanglement • Requires 2 bits of forward communication to the receiver

22 Quantum Communication and Quantum Networks

is the process by which quantum information can be transmitted from one location to another, Teleportation with the help of classical communication and previously shared quantum entanglement between two parties.

23 Quantum Communicaon and Quantum Networks Long distance entanglement Quantum repeaters:

|�⟩ |�⟩ Alice Bob �

� � in fiber

� decays exponentially fast in distance

24 Quantum Communicaon and Quantum Networks

Quantum repeaters: • How to send qubits over long distances? • Amplifiers cannot be used since qubits cannot be Quantum copiedis different- known as the no-cloning theorem.

No copying! Short lifetimes, difficult to manipulate many qubits 25

Entanglement works differently - Inherently connected! QuantumQuantum Communication Repeater and Quantum Networks

Quantumquantum repeaters: memories to store qubits • How to send qubits for long distances? generate• generate link link Bell states Bell(entanglements states ) (entanglements)• Timing coordinaon: qubits arriving at the same me at the mid point • Or storage: wait unl both qubits arrived propagate• propagate entanglements entanglements • Original entanglement is consumed destructive Bell state measurement • Classical communicaon note:• from repeaterthe mid point does to the endnotpoints know superposition state

26 Quantum CommunicationTransmitting Quantumand Quantum Information Networks Suppose Alice wants to send qubit to Bob

Alice Bob

Quantum repeaters: End-to-end entanglements • In essence, a quantum repeater protocol + executes three operations: Key ingredient for a quantum repeater: • Entanglement distribution; Entanglement SwappingTeleportation*

• Entanglement purification; *Quantum teleportation consumes a resource: an entanglement. • Entanglement swapping.

End node Repeater End node

Resources: • Timing coordination: qubits arriving at the same time at the27 mid point • Or, storage: wait until both qubits arrived • Classical communication from the mid point to the end points • Original entanglement is consumed Quantum Communication and Quantum Networks

End-to-end entanglementsEntanglement CreationBob Alice link-level entanglements CarolBob qubit to be transmitted

Alice measurement CarolBob

Alice CarolBob end-to-end entanglement

28 Quantum Communicaon and Quantum NetworksTeleportation Teleportation Alice CarolBob

Alice CarolBob

? (1,0)

Alice CarolBob

• Consumes the entanglement • Requires 2 bits of forward communicaon to the receiver 29 Quantum Communication and Quantum Networks

End nodes • the quantum processors connected to the quantum Internet. • These may range from extremely simple nodes that can only prepare and measure single qubits to large-scale quantum computers. • End nodes may themselves act as quantum repeaters, although this is not a requirement. • All nodes can communicate classically—for example, over the classical internet—in order to exchange control informaon.

30 RESEARCH

◥ transmitting qubits over long distances a truly REVIEW formidable endeavor. Because qubits cannot be copied or amplified, repetition or signal am- plification are ruled out as a means to overcome QUANTUM INFORMATION imperfections, and a radically new technological development—such as quantum repeaters—is needed in order to build a quantum internet Quantum internet: A vision (Figs. 2 and 3) (5). We are now at an exciting moment in time, akin to the eve of the classical internet. In late for the road ahead 1969, the first message was sent over the nas- cent four-node network that was then still re- 1* 1 1,2 Stephanie Wehner , David Elkouss , Ronald Hanson ferred to as the Advanced Research Projects Agency Network (ARPANET). Recent technolog- The internet a vast network that enables simultaneous long-range classical — ical progress (6–9)nowsuggeststhatwemaysee communication has had a revolutionary impact on our world. The vision of a quantum — the first small-scale implementations of quan- internet is to fundamentally enhance internet technology by enabling quantum tum networks within the next 5 years. communication between any two points on Earth. Such a quantum internet may operate in At first glance, realizing a quantum internet parallel to the internet that we have today and connect quantum processors in order to (Fig. 3) may seem even more difficult than build- achieve capabilities that are provably impossible by using only classical means. Here, we ing a large-scale quantum computer. After all, we propose stages of development toward a full-blown quantum internet and highlight might imagine that in full analogy to the clas- Downloaded from experimental and theoretical progress needed to attain them. sical internet, the ultimate version of a quantum internet consists of fully fledged quantum com- he purposeQuantum of a quantum internet is to Communicaoninclude secure access to remote quantum computers thatand can exchange an essentially arbi- enable applications that are fundamen- puters (2), more accurate clock synchronization trary number of qubits. Thankfully, it turns out tally out of reach for the classical internet. (3), and scientific applications such as com- that many quantum network protocols do not A quantum internet could thereby supple- bining light from distant telescopes to improve require large quantum computers to be real- Quantum Networks http://science.sciencemag.org/ T ment the internet we have today by using observations (4). As the development of a quan- ized; a quantum device with a single qubit at quantum communication, but some researchers tum internet progresses, other useful applica- the end point is already sufficient for many go further and believe all communication will tions will likely be discovered in the next decade. applications. What’s more, errors in quantum eventually be done over quantum channels (1). Central to all these applications is that a quan- internet protocols can often be dealt with by The best-knownQuantum application ofKey a quantum Distribution in- tum internet(QKD) enables us to transmit quantum using classical rather than quantum error cor- ternet is quantum key distribution (QKD), which bits (qubits), which are fundamentally differ- rection, imposing fewer demands on the control enables two• remote network nodes to establish ent from classical bits. Classical bits can take and quality of the qubits than is the case for a an encryption keyThe whose most security practical, relies only on commerciallyonly two values, 0 or 1,attractive whereas qubits canuse be offully quantum fledged quantum computer. The reason the laws of quantumnetworks mechanics. in This the is im-nearin term. a superposition of 0 and 1 at the same time. why quantum internet protocols can outperform possible with the classical internet. A quantum Importantly, qubits cannot be copied, and any classical communication with such relatively internet, however, has many other applications attempt to do so can be detected. It is this fea- modest resources is because their advantages • The main objective in QKD is generates shared, secret random (Fig. 1) that bring advantages that are unattain- ture that makes qubits naturally well suited for rely solely on inherently quantum properties on October 16, 2019 able with a classicalnumbers network. Such between applications twosecurity distant applications parties. but at the same time makes such as quantum entanglement, which can be • Uses quantum mechanics to detect the presence or absenceexploited of alreadyan with very few qubits. By con- eavesdropper. trast, a quantum computer must feature more Fig. 1. Applications of a quantum qubits than can be simulated on a classical com- internet. One application of a quan- puter in order to offer a computational advantage. tum internet is to allow secure Given the challenges posed by the development of access to remote quantum com- aquantuminternet,itisusefultoreflectonwhat puters in the cloud (2). Specifically, a capabilities are needed to achieve specific quan- simple quantum terminal capable of tum applications and what technology is required preparing and measuring only single to realize them. qubits can use a quantum internet to Here, we propose stages of development access a remote quantum computer toward a full-blown quantum internet. These in such a way that the quantum stages are functionality driven: Central to their computer can learn nothing about definition is not the difficulty of experimentally which computation it has performed. achieving them but31 rather the essential question Almost all other applications of a quantum internet can be understood from two special features of of what level of complexity is needed to actually quantum entanglement. First, if two qubits at different network nodes are entangled with each enable useful applications. Each stage is inter- other, then such entanglement enables stronger than classical correlation and coordination. For esting in its own right and distinguished by a example, for any measurement on qubit 1, if we made the same measurement on qubit 2, then we specific quantum functionality that is sufficient instantaneously obtain the same answer, even though that answer is random and was not to support a certain class of protocols. To illus- determined ahead of time. Very roughly, it is this feature that makes entanglement so well suited for trate this, for each stage we give examples of tasks that require coordination. Examples include clock synchronization (3), leader election, and known application protocols in which a quantum achieving consensus about data (53), or even using entanglement to help two online bridge players internet is already known to bring advantages. coordinate their actions (39). The second feature of quantum entanglement is that it cannot be 1 shared. If two qubits are maximally entangled with each other, then it is impossible by the laws of QuTech, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands. 2Kavli Institute of quantum mechanics for a third qubit to be just as entangled with either of them. This makes Nanoscience, Delft University of Technology, Post Office Box entanglement inherently private, bringing great advantages to tasks that require security such as 5046, 2600 GA Delft, Netherlands. generating encryption keys (12) or secure identification (24, 25). *Corresponding author. Email: [email protected]

Wehner et al., Science 362, eaam9288 (2018) 19 October 2018 1 of 9 Quantum Communication and Quantum Networks

Inherently private Quantum Key Distribution (QKD) • An important and unique property of QKD is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key; • This results from a fundamental property of quantum mechanics: • the process of measuring a quantum system, in general, disturbs the system. • The first QKD protocol was proposed in 1984 and since then, more protocols have been proposed: • BB84, developed by Charles Bennett and Gilles Brassard; • E91, proposed by Artur Ekert.

32 Quantum Communicaon and Quantum Networks

QKD Implementations • Well beyond the experimental phase; • Commercial products are available, and metropolitan-area testbed networks exist in: • Boston, Vienna, Geneva, Barcelona, Durban, Tokyo, several sites in China and elsewhere throughout the world. • QKD has also been integrated into: • custom encryption suítes; • Internet standard IPsec suíte; • And has been proposed for use with the TLS protocol.

33 Quantum Networks and Quantum Internet

Characteristics Challenges • Enable to transmit quantum bits; • Qubits can be entangled with each • Transmit qubits over long distances other enabling stronger correlation and coordination • Achieve more useful quantum • Qubits cannot be copied/amplified; applicaons and • Quantum network protocols do not require large quantum computer • deﬁne technology required to • Errors in quantum internet realize them. protocols can often be dealt with by using classical error correction

34 Quantum Networks and Quantum Internet

The basic structure of a quantum network and more generally a quantum Internet is analogous to a classical network.

Quantum channels, quantum repeaters (quantum routers/switches) and end nodes.

Layering is a natural means of the associated modularity allows us to replace individual functions more or less dividing functionality independently.

35 Quantum Networks Quantum Network Stack and Quantum Internet Application Quantum Application Protocols

• Some preliminary functional Transport End-to-end Qubit Delivery allocation of a quantum network Long-distance Entanglement Generation stack has been proposed: Network • Stages of development toward a full-blown quantum Internet, Link Entanglement Generation on a Link proposed by Stephanie Wehner et al.; Physical Quantum Device Layer • Quantum Recursive Network Architecture (QRNA), proposed by Van Meter et al.;

36 Evolution Phases RESEARCH | REVIEW

• Short term: one may optimize both repeaters andFig. 4.end Stagesnodes of quantumrelatively to attack the protocol, and remains secure at any independentlyinternet: development. A spe- point in the future, even if such a quantum com- cific implementation of a quan- Øsimple end nodes puter becomes available later on. This is provably tum internet may, like for a Øpowerful repeaters impossible when using classical communication. classical network, be optimized The BB84 QKD (11) protocol can be realized by • Near-term: forquantum distance,internet functionality,may or be using only single-qubit preparations and measure- optimized forboth.shorter The termdistances network: ments tolerating some amount of post-selection p Øfor example, pan-European commonly refers to a situation (19). For known protocols in this stage, eT + eM ≤ Øpowerful endthatnodes goes beyond point-to-point 0.11 is sufficient and can be estimated by testing • Long term:communication;a full-blown theworldwide objective of for only a small number of states (20). In practice, quantum interneta network. is to provide any end single-qubit preparationcanbereplacedwithat- Ø nodes (connected to the *Funcionality driven stages of Quantum Internet according Stephanie Wehner et al. tenuated laser pulses, using also decoy-state BB84 quantum repeaters need to be able to [S. Wehner and Hanson 2018]. support thenetwork)functionality with theof meanseach stage to exchange. data, making three end nodes the smallest instance of a true to guarantee security (21). QKD is commercially network. Outside the laboratory, only trusted repeater networks (first stage) have been realized in available at short distances by using standard metropolitan areas (62–65).Two single far-away end nodes (68) have also been connected via satellite.37 telecom fibers (22), and a variety of protocols are known [(23), survey]. Another class of protocols in this stage is in the So far, most application protocols have only other interesting tasks. Informally, this stage domain of two-party cryptography. Here, there is been analyzed for perfect parameters. As such, allows any node to prepare a one-qubit state no eavesdropper, but rather Alice and Bob them- the exact requirements of many application and transmit the resulting state to any other selves do not trust each other. An example of such

protocols on these parameters have not yet been node, which then measures it (definition is a task is secure identification, in which Alice Downloaded from determined and deserve future investigation. Al- provided in Table 1). Transmission and mea- (a potentially impersonating user) may wish to though functionality-driven stages make de- surement are allowed to be post-selected; that identify herself to Bob (a potentially malicious mands on the communication links and quantum is, a signal that the qubit is lost may be gen- server or automated teller machine) without re- repeaters, it will not be important in this sec- erated instead. For instance, the receiving node vealing her authentication credentials (24, 25). It tion how these links are realized; they may be is allowed to ignore nondetection events and is known that even by using quantum communi- realized by direct transmission in fiber, by being conclude that such qubits are lost. If the sen- cation, such tasks cannot be implemented secure- relayed by any kind of quantum repeater, or der can prepare an entangled state of two qubits, ly without imposing assumptions on the power of http://science.sciencemag.org/ even by means of teleportation using preshared then this stage also includes the special case the adversary (26–28). Classical protocols rely on entanglement. What matters is that these links in which the sender transmits the first and se- computational assumptions, whose security against can be used to generate the necessary quantum cond qubit to two different nodes in the network an attacker who holds a quantum computer is states for a specific stage. (or to another node and itself). Such entangle- unclear. Nevertheless, it is possible to achieve ment distribution is then also post-selected. provable security for all such relevant tasks by Trusted repeater networks Such a post-selected prepare-and-measure func- sending more qubits than the adversary can store The first stage differs substantially from the tionality is not equivalent to transmitting arbi- easily within a short time frame, which is known others in the sense that it does not allow the trary qubits across the network (18). The task of as the bounded (29)ormoregenerallynoisy- end-to-end transmission of qubits. Nevertheless, transmitting arbitrary qubits demands the abil- storage model (30, 31). This assumption only from a technological perspective, trusted re- ity to transfer an unknown state Y (which the needs to hold during the execution of the proto-

peater networks can form an interesting stepping sender does not know how to prepare)j i determinis- col, and security is preserved into the future even on October 16, 2019 stone toward a quantum internet, spurring in- tically to the receiver—that is, no post-selection on if the adversary later obtains a better quantum frastructure deployment and engineering devel- detection events is allowed. memory. There exist protocols for which it is suf- opments; depending on the underlying technology, The classical reader may wonder what is the ficient to prepare and measure single qubits, in trusted repeaters (10) can be upgraded to true use of transmitting qubits at all if there is a which the sufficient values of p, eM, eT (Table 1) quantum repeaters later on. procedure for the sender to prepare the state Y . depend on the storage assumption (32). Specifically, a trusted repeater network (some- After all, we might imagine that the sender sim-j i Other known protocols in this stage include times called a trusted node network) has at ply sends classical instructions for this procedure position verification (33); weakened forms of two- least two end nodes and a sequence of short to the receiver, who then prepares the qubit it- party cryptographic tasks that can form building distance links that connect nearby intermediary self. The difference between such a classical pro- blocks, such as imperfect bit commitments (34); repeater nodes. Each pair of adjacent nodes tocol and sending different quantum states Y and coin-flipping (35). Here, the requirements in j i uses QKD (11–13) to exchange encryption keys. directly is that in the latter case, an eavesdropper, terms of p, eM,andeT have not been analyzed yet; These pairwise keys allow the end nodes to or indeed the receiver, cannot make a copy of Y no task exists for which a full set of necessary generate their own key, provided that all inter- without disturbing the quantum state. This meansj i and sufficient conditions on these parameters is mediary nodes are trusted (14). A first step that attempts to gain information from Y by an known. toward upgrading such networks could be mea- eavesdropper may be detected, enablingj QKD.i surement device–independent QKD (15–17), which Entanglement distribution networks is a QKD protocol that is secure even with un- Application protocols The third stage allows the end-to-end creation trusted measurement devices that can be im- This stage is already sufficient to realize proto- of quantum entanglement in a deterministic or plemented with standard optical components cols for many interesting cryptographic tasks, heralded fashion, as well as local measurements. and sources (17); this protocol already incor- as long as the probability of loss (p)andthein- The end nodes require no quantum memory for porates some useful ingredients for later stages, accuracies in transmission (eT) and measure- this stage (Table 1). such as two-photon Bell measurements. ment (eM)(Table1)aresufficientlylow.Themost The term “deterministic entanglement gener- famous of such tasks is QKD, which provides a ation” refers to the fact that the process succeeds Prepare and measure networks solution to the task of generating a secure en- with (near) unit probability. Heralding is a slight- This stage is the first to offer end-to-end quan- cryption key between two distant end nodes ly weaker form of deterministic entanglement tum functionality. It enables end-to-end QKD (Alice and Bob) (11–13). QKD is secure even if the generation in which we signal the successful gen- without the need to trust intermediary repeater eavesdropper trying to learn the key has access to eration of entanglement with an event that is in- nodes and already allows a host of protocols for an arbitrarily large quantum computer with which dependent of the (immediate) measurement of the

Wehner et al., Science 362, eaam9288 (2018) 19 October 2018 3 of 9 Quantum Network Stack

RESEARCH | REVIEW

Important to: photon loss and decoherence during transmis- indeed be the dawn of a future large-scale quan- • Enable widespread use and application sion (97–100). The main advantage of such a tum internet. development: scheme is that the classical two-way communication of standard repeater schemes (necessary REFERENCES AND NOTES to convey the heralding signal of whether or not • No such network stack presently exists for a 1. D. Castelvecchi, The quantum internet has arrived (and it quantum internet: the photons arrived at the stations) becomes ob- hasn’t). Nature 554, 289–292 (2018). solete. The communication rates of these schemes 2. A. Broadbent, J. Fitzsimons, E. Kashefi, 50th Annual IEEE • Only some basic elements have been noted. are therefore potentially much higher. However, Symposium on Foundations of Computer Science, 2009. the experimental demands seem daunting at pre- (IEEE, 2009), pp. 517–526. • Examples of why a new stack is required: 3. P. Kómár et al., A quantum network of clocks. Nat. Phys. 10, sent; for encoding the qubit, the near-deterministic 582–587 (2014). doi: 10.1038/nphys3000 • Mapping between classical control information generation of a many-photon cluster state is re- 4. D. Gottesman, T. Jennewein, S. Croke, Longer-baseline (header) and the underlying qubits quired, which is far beyond the state of the art telescopes using quantum repeaters. Phys. Rev. Lett. 109, (101). Furthermore, becausetheseschemesrequire 070503 (2012). doi: 10.1103/PhysRevLett.109.070503; • The use of error detection at the link layer of the pmid: 23006349 classical network stack does not easily translate to a quantum error correction, they will only work if 5. H. J. Kimble, The quantum internet. Nature 453, 1023–1030 the error thresholds associated with the desired realistic quantum network. (2008). doi: 10.1038/nature07127; pmid: 18563153 Fig. 5. Possible elements of a future quan- transmission qualities are met, thus placing more 6. A. I. Lvovsky, B. C. Sanders, W. Tittel, Optical quantum memory. Nat. Photonics 3, 706–714 (2009). doi: 10.1038/ tum network stack. 38 stringent requirements on the control and readout nphoton.2009.231 fidelities within the repeater nodes. That being 7. T. Northup, R. Blatt, Quantum information transfer using said, theory research (102)inthisdirectionislike- photons. Nat. Photonics 8, 356–363 (2014). doi: 10.1038/ the feasibility of such conversion; the current ly to yield more insights, and experimental pro- nphoton.2014.53 8. D. D. Awschalom, R. Hanson, J. Wrachtrup, B. B. Zhou, challenge is to realize a robust and high-efficiency gress may bring such schemes closer to reality in Downloaded from Quantum technologies with optically interfaced solid-state (say, >50%) converter that exhibits a high signal- the future. spins. Nat. Photonics 12, 516–527 (2018). doi: 10.1038/ to-noise ratio (say, >100). Last, the end nodes that are currently being s41566-018-0232-2 As an alternative to the above systems with developed may also function themselves as 9. A. Reiserer, G. Rempe, Cavity-based quantum networks with intrinsic optical interface, the end nodes could be repeaters. single atoms and optical photons. Rev. Mod. Phys. 87, 1379–1418 (2015). doi: 10.1103/RevModPhys.87.1379 formed from a quantum processor with qubit 10. L. Salvail et al., Security of trusted repeater quantum key frequencies in the microwave domain, such as a Network stack requirements distribution networks. J. Comput. Secur. 18, 61–87 (2010). superconducting qubit circuit, in combination In order to enable widespread use and applica- doi: 10.3233/JCS-2010-0373 http://science.sciencemag.org/ 11. C. H. Bennett, G. Brassard, International Conference on with a microwave-to-optical conversion process. tion development, it is essential to develop meth- Computer System and Signal Processing, IEEE, 1984 (1984), The physics of such a conversion—for instance, ods that allow quantum protocols to connect to pp. 175–179. by use of mechanical resonators (88, 89)oratom- the underlying hardware implementation trans- 12. A. K. Ekert, Quantum cryptography based on Bell’s theorem. ic transitions (90)—is currently being investigated parently and to make fast and reactive decisions Phys. Rev. Lett. 67, 661–663 (1991). doi: 10.1103/ PhysRevLett.67.661; pmid: 10044956 in many laboratories. for generating entanglement in the network in 13. S. Wiesner, Conjugate coding. ACM SIGACT News 15, 78–88 order to mitigate limited qubit lifetimes (Fig. 5). (1983). doi: 10.1145/1008908.1008920 Quantum repeater requirements Classically, this is achieved by a series of layered 14. V. Scarani et al., The security of practical quantum key Quantum repeater stations need to improve the protocols such as the Transmission Control distribution. Rev. Mod. Phys. 81, 1301–1350 (2009). doi: 10.1103/RevModPhys.81.1301 rate of photonic qubit transfer. The requirements Protocol/Internet Protocol (TCP/IP) (103) that 15. E. Biham, B. Huttner, T. Mor, Quantum cryptographic network for quantum repeaters are similar to but less provide an abstraction that ultimately allows ap- based on quantum memories. Phys. Rev. A 54, 2651–2658

strict than for the end nodes. In particular, de- plication protocols to exchange data between two (1996). doi: 10.1103/PhysRevA.54.2651; pmid: 9913773 on October 16, 2019 pending on the exact architecture [(91), review], end nodes without havingtoknowanydetailson 16. S. L. Braunstein, S. Pirandola, Side-channel-free quantum key distribution. Phys. Rev. Lett. 108, 130502 (2012). the storage of quantum states may only be re- how this connection is actually realized. No such doi: 10.1103/PhysRevLett.108.130502; pmid: 22540685 quired for the time needed to establish entan- network stack presently exists for a quantum 17. H.-K. Lo, M. Curty, B. Qi, Measurement-device-independent glement between the nearest active nodes; this internet, and only some basic elements have quantum key distribution. Phys. Rev. Lett. 108,130503 storage time can deviate substantially from that been noted (104). As a trivial example on why a (2012). doi: 10.1103/PhysRevLett.108.130503; pmid: 22540686 required for the end nodes. Also, the qubit pro- new stack is required for a quantum network, the 18. M. M. Wilde, Quantum Information Theory (Cambridge Univ. cessing capabilities required are limited, and first novel feature is a mapping between classical Press, 2013). therefore systems different from the ones above control information (header) and the underlying 19. C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, can be considered. As a prime example, an ensem- qubits. By contrast, classically a header and data H. M. Wiseman, One-sided device-independent quantum key distribution: Security, feasibility, and the connection with ble of atoms and ions either in gas phase or in a may be nicely combined in one piece of data to be steering. Phys. Rev. A 85, 010301 (2012). doi: 10.1103/ solid can be used as an on-demand quantum transmitted. Another example is the use of error PhysRevA.85.010301 memory (92). If the memory can herald the ar- detection at the link layer of the classical network 20. A. Gilchrist, N. K. Langford, M. A. Nielsen, Distance measures rival of a photon and store the photon’squantum stack that does not easily translate to a realistic to compare real and ideal quantum processes. Phys. Rev. A 71, 062310 (2005). doi: 10.1103/PhysRevA.71.062310 state, photon loss can be efficiently mitigated. quantum network. Clearly, error detection can 21. H.-K. Lo, X. Ma, K. Chen, Decoy state quantum key Storage and on-demand retrieval have already theoretically be realized by using quantum error- distribution. Phys. Rev. Lett. 94, 230504 (2005). been achieved (93–96), although efficiencies are correcting codes, but this method may be prohib- doi: 10.1103/PhysRevLett.94.230504; pmid: 16090452 still to be improved. Such memories also allow itively expensive in practice, and other methods 22. A. Extance, Fibre Systems (2017); www.fibre-systems.com/ feature/quantum-security. for multiplexing within a single device. Further- 105 ( )maybemoresuitable.Thesearejusttwo 23. E. Diamanti, H.-K. Lo, B. Qi, Z. Yuan, Practical challenges in more, they are compatible with current-day down- simple examples of the challenges involved in quantum key distribution. NPJ Quantum Information 2, 16025 conversion sources for entangled photon pairs. designing such a network stack, calling for sub- (2016). doi: 10.1038/npjqi.2016.25 Current challenges are to combine heralding and stantial development. 24. I. Damgård, S. Fehr, L. Salvail, C. Schaffner, Secure on-demand high-efficiency retrieval with long identification and QKD in the bounded-quantum-storage Although it is hard to predict what the exact model. Theor. Comput. Sci. 560, 12 (2014). doi: 10.1016/ coherence times. physical components of a future quantum inter- j.tcs.2014.09.014 Aradicallydifferentapproachtoquantumre- net will be, it is likely that we will see the birth of 25. F. Dupuis, O. Fawzi, S. Wehner, Entanglement sampling and peaters has emerged in recent years in which the the first multinode quantum networks in the next applications. IEEE Trans. Inf. Theory 61, 1093–1112 (2014). quantum state of interest is encoded in multiple few years. This development brings the exciting doi: 10.1109/TIT.2014.2371464 26. D. Mayers, Unconditionally secure quantum bit commitment photons so that error correction performed at opportunity to test all the ideas and function- is impossible. Phys. Rev. Lett. 78, 3414–3417 (1997). the repeater stations can erase errors caused by alities that so far only exist on paper and may doi: 10.1103/PhysRevLett.78.3414

Wehner et al., Science 362, eaam9288 (2018) 19 October 2018 7 of 9

Quantum Recursive

Network Architecture

(QRNA)

• QRNA’s organizing principle is * 2011, Van Meter, Touch e Horsman recursion;

• The most radical difference from VAN_METER_LAYOUT_Layout 1 8/1/13 2:21 PM Page 69 classical networks arises from the need to extend message Five-layer model role Purify-and-swap layer Application APP APP Application Error management PC PC Purification control semantics: Remote state composition ESC ESC ESC Entanglement swapping control Error management PC PC PC PC Purification control Remote state composition ESC ESC ESC ESC ESC ESC Entanglement swapping control • Messages in QRNA will carry requests Error management PC PC PC PC PC PC PC PC Purification control Link-level entanglement EC EC EC EC EC EC EC EC Entanglement control more explicitly: Physical PE PE PE PE PE PE PE PE Physical entanglement Node A Node B Node C Node D Node E Figure 4. Protocol layers and their interaction in purify-and-swap repeaters in a five-node four-hop chain. The left labels indicate the • please build this state for me, and dispose of model layer represented, and the boxed labels and right labels indicate the protocol name for purify-and-swap repeaters. Double-head- ed arrows indicate that bidirectional classical communication is required. Only the physical layer is quantum, shown propagating left it like so once it is built. to right. *Proposed by Van Meter, Touch and Horsman State relocation across a network would be approach is to adapt Dijkstra’s shortest path first sufficient for some applications. One-way tele- algorithm to repeater networks. portation from a client to a server is sufficient The layered communication approach impacts for universal blind quantum computation, in whether paths are established before communi- which the server is oblivious to the computa- cation or on the fly. As shown in Fig. 4, purify tion it performs for the client. State relocation and swap requires continuous actions distributed 39 also appears to extend smoothly from unen- among the nodes along the path, so it assumes tangled networks. Applications that need that communications will follow the same path simultaneous long-distance entangled states for the entire session. Pre-establishment of a must build them, because state relocation does path simplifies naming for mid-session opera- not provide entangled states. State relocation tions and simplifies predictable resource alloca- does not demand long-lived memory unless tion by assigning in-process quantum states to the session architecture itself does, but it also specific sessions. On-the-fly path construction is cannot easily take advantage of resources in more flexible but could result in communications the middle of the network to operate more being interrupted if available memory or quan- efficiently. tum states are exhausted, say, by competing con- Distributed state generation supports a more nections. general distributed computation model. It works well with both two-party and multiparty entan- Identifiers — Networks naturally require names gled states. However, in the basic form it for the nodes or communication endpoints. requires long-lived memory. Unlike the Internet, purify-and-swap end nodes Asynchronous distributed state generation is communicate directly with nodes along the path. actually the most general model, subsuming On the Internet, a packet is directed to tran- both of the above. This model, which QRNA sit a particular subnet (Internet autonomous adopts, provides the most direct match to system), rather than given a complete hop-by- applications such as entanglement-based quan- hop source route. QRNA’s recursive naming tum key distribution, in which long-distance allows an operation, such as Bell pair creation Bell pairs are measured at each end soon after or entanglement swapping, to be similarly creation. directed to a subnetwork rather than to a specific node. Paths then can be transparently relo- Links, Nodes, and State — Classical network cated within the subnetwork. This partially architectures are typically composed of three relaxes the path constraint, simplifying end fundamental elements: nodes, links, and state. node knowledge of network components and Nodes represent the communicating parties, or returning local operation decisions to the local relays that assist those parties. Links represent neighborhood. one-hop communication paths, and state repre- The entangled states built within the network sents the information being communicated. also must be named, to facilitate their manage- Nodes in a quantum network are much like ment and delivery to applications. On the Inter- their classical counterparts, except that they net, packets are mapped to a connection using a include memory that can encode qubits. Some tuple consisting of node addresses, a connection architectures support nodes that interact with identifier (port numbers), and possibly an appli- quantum state but avoid needing direct quantum cation-level identifier. In quantum networks, memory. Links in a quantum network transmit such a tuple may not yet exist because a dis- both quantum state as well as classical informa- tributed state, such as a Bell pair in the middle tion. Both types of information are required to of the network, might not yet be assigned to support teleportation. serve a particular end-to-end session. QRNA is designed to accommodate this delayed associa- Paths — Multihop networks require a means of tion (a type of late binding) and to reassign state selecting a path through the network [14]. One identifiers when necessary.

IEEE Communications Magazine • August 2013 69 State of the art • Quantum Cryptography (QKD): Key Distribution • Non Device Independent • Metropolitan-area testbed networks Status: • Commercial at short (~100km) distances (idQuantique, Huawei, Toshiba, Mitsubishi, ....) Where are we • Lab ~300kms • Entanglement over a distance of ~ 1400km via now? satellite Grand Challenges: •QuantumDistance – want communication to communicate over ––state statelong distances ofof thethe artart • Functionality – want to do more than QKD

Quantum Cryptography (QKD) –– nonnon DI:DI: KeyKey DistributionDistribution

Status: •• Commercial at short (~100kms) distancesdistances ((idQuantiqueidQuantique,, Huawei,Huawei, Toshiba,Toshiba, NEC,NEC, Mitsubishi,Mitsubishi, ….)….) •• Lab ~300kms Survey by Alleaume et al, Theoretical ComputerComputer Science,Science, 560560 (2014),(2014), pp.pp. 6262--8181

Grand Challenges: •• Distance – want to communicate overover longlong distancesdistances •• Functionality – want to do more thanthan QKDQKD

Metropolitan-area testbed

networks

Boston-area network • the world’s first deployed QKD network • supported by DARPA

• 10 nodes running several different QKD implementations • “A” nodes contain the transmitters and “B” nodes contain the receivers . • some nodes are multiple hops away. • BBN developed a quantum key relay protocol to allow those nodes to share secret Keys.

Planned test link Delft – Den Haag

MetropolitanPossible- areaNetwork testbed Expansion • Upgrade existing nodes – form a network networks KPN PB400: node location • World’s first network connecting quantum computers TU Delft: • Multiple processor nodes node location • Direct QKD links between neighbouring nodes to authenticate control Delft – Den Haagtraffic • World’s first quantum network stack demonstration • Make 2 processor• Including nodes universalthat are programmability prepared for KPN telephone exchange: future upgrades• Make platform available on the internet detector location • Make use of existing telecom (dark) fibers • Make 2 processor nodes that are prepared for future upgrades • World record in linking quantum processors at a distance • Generation of entanglement between the 2 • Make use of existing telecom (dark) fibers nodes • Generation of entanglement between the 2 nodes Possible Network Expansion • Gain experience • World’s first network connecting quantum computers • Direct QKD links between neighbouring nodes to authenticate control traffic • World’s first quantum network stack demonstration

42 Research Challenges Some networking challenges: • Link layer • No-broadcasting theorem: impossibility of transmitting quantum information to more than a single destination; • Routing • novel quantum routing metrics; • Static vs opportunistic routing; • Network layer • new entangled pairs need to be created and distributed between the source and the destination for each additional qubits need to be teleported; • Fast and reactive control plane for generating entanglement

43 Research Challenges

More networking challenges: • Modeling and performance analysis • Stateless vs stateful control • Data, control plane design • SDN • Quantum data plane • programmable quantum switches • Measurement, management • Security • Understanding application requirements

44 Research Challenges

The main challenges in scaling networks to Internet-scale and beyond are: • Heterogeneity • especially of deployed technologies and local conditions; • sheer scale • affecting routing and naming in particular; • dealing with out-of-date information • e.g. routing or congestion; • meeting the needs of participating organizations • such as privacy, policies and autonomous management; • and misbehaving nodes on the network • deliberate or accidental.

45 China: • China’s Quantum Experiments at Space Scale (Micius) • National Laboratory for Quantum Information Science (Hefei) • 76 billion Yuan Europe: Quantum initiatives Quantum • Quantum Technology Flagship China: • one billion euros initiatives China’s Quantum2017 Experiments-2027 at Space Scale (Micius) USA: National Laboratory for Quantum Information Science • National Quantum Initiative Act (Hefei) 76 billion •Yuan1.25 billion dolllars 2019-2029 Europe: Quantum Technology• National FlagshipScience Foundation • Research Center for Quantum Networks one billion euros 2017-2027 USA: National Quantum Initiative Act 1.25 billion dolllars 46 2019-2029 Simulators

• To explore quantum networking: • NetSquid: Network Simulator for Quantum Information using Discrete events. • http://www.netsquid.org

• To explore quantum applications: • Application level simulator - SimulaQron Download • http://www.simulaqron.org

47 Thanks! Questions?