Towards a Distributed Quantum Computing Ecosystem(Invited Paper)

Daniele CuomoUniversity of Naples Federico II

daniele.cuomo@unina.it

Marcello CaleffiUniversity of Naples Federico II

marcello.caleffi@unina.it

Angela Sara CacciapuotiUniversity of Naples Federico IIangelasara.cacciapuoti@unina.it

Abstract—The Quantum Internet, by enabling quantum com-munications among remote quantum nodes, is a network capableof supporting functionalities with no direct counterpart in theclassical world. Indeed, with the network and communicationsfunctionalities provided by the Quantum Internet, remote quan-tum devices can communicate and cooperate for solving chal-lenging computational tasks by adopting a distributed computingapproach. The aim of this paper is to provide the reader with anoverview about the main challenges and open problems arisingwith the design of a Distributed Quantum Computing ecosystem.For this, we provide a survey, following a bottom-up approach,from a communications engineering perspective. We start byintroducing the Quantum Internet as the fundamental underlyinginfrastructure of the Distributed Quantum Computing ecosystem.Then we go further, by elaborating on a high-level systemabstraction of the Distributed Quantum Computing ecosystem.Such an abstraction is described through a set of logical layers.Thereby, we clarify dependencies among the aforementionedlayers and, at the same time, a road-map emerges.

I. INTRODUCTION

Nowadays, a tremendous amount of heterogeneous playersentered the quantum race, ranging from tech giants - such asIBM and Google in fierce competition to build a commercialquantum computer - to states and governments, with massivepublic funds to be distributed over the next years [1], [2], [3],[4].

In 2017, the European Commission launched a e1-billionflagship program to support the quantum research for ten yearsstarting from 2018, and a first e132-million tranche is beingprovided during the following three years [5]. In 2018, theUnited States of America launched the National QuantumInitiative funded with $1.2-billion over ten years and Chinais keeping up, investing billions to commercialize quantumtechnologies [6].

These huge efforts are justified by the disruptive potentialof a quantum computer, beyond anything classical computerscould ever achieve. Indeed, by exploiting the rules of quantummechanics, a quantum computer can tackle classes of problemsthat choke conventional machines. These problems includechemical reaction simulations, optimization in manufacturingand supply chains, financial modeling, machine learning andenhanced security [7], [8], [9]. Hence, the quantum computinghas the potential to completely change markets and industries.

At the end of 2019, Google achieved the so-called quan-tum supremacy1 with a 54-qubits quantum processor, named

1The term was coined by J. Preskill in 2012 [10] to describe the momentwhen a programmable quantum device would solve a problem that cannot besolved by classical computers, regardless of the usefulness of the problem.

Sycamore, by sampling from the output distribution of 53-qubits random quantum circuits [11]. By neglecting someperformance-enhancing techniques as pointed out by IBM[12], [13], Google estimated that “a state-of-the-art supercom-puter would require approximately 10,000 years to perform theequivalent task” that required just 200 seconds on Sycamore.

By ignoring the noise effects and by coarsely oversimpli-fying, the computing power of a quantum computer scalesexponentially with the number of qubits that can be embeddedand interconnected within [2]. And one of the reasons laysin a principle of quantum mechanics known as superpositionprinciple. Specifically, a classical bit encodes one of twomutually exclusive states - usually denoted as 0 and 1 - beingin only one state at a certain time. Conversely, a qubit can bein an extra mode - called superposition i.e., it can be in acombination of the two basic states [2], [3].

Hence – thanks to the superposition principle – a qubitoffers richer opportunities for carrying information and com-puting, since it can do more than just flipping between 0 and1. And this quantum advantage grows exponentially with thenumber of qubits. In fact, while n classical bits are only inone of the 2n possible states at any given moment, an n-qubitregister can be in a superposition of all the 2n possible states.

To give a flavor of the above, let us consider one ofthe killer applications of the quantum computing: chemicalreaction simulation [14]. As highlighted in [15], the amount ofinformation needed to fully describe the energy configurationsof a relatively simple molecule such as caffeine is astoundinglylarge: 1048 bits. For comparison, the number of atoms inthe Earth is estimated between 1049 and 1050 bits. Hence,describing the energy configuration of caffeine at one singleinstant needs roughly a number of bits comparable to 1 to10 per cent of all the atoms on the planet. But this energyconfiguration description becomes suddenly feasible with aquantum processor embedding roughly 160 noiseless qubits,thanks to the superposition principle.

Unfortunately, qubits are very fragile and easily modified byinteractions with the outside world, via a noise process knownas decoherence [16], [3]. Indeed, decoherence is not the onlysource of errors in quantum computing. Errors practically arisewith any operation on a quantum state. However, isolatingthe qubits from the surrounding is not the solution, sincethe qubits must be manipulated to fulfill the communicationand computing needs, such as reading/writing operations.Moreover, the challenges for controlling and preserving thequantum information embedded in a single qubit get harder

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as the number of qubits within a single device increases,due to coupling effects. In this regard, Quantum Error Cor-rection (QEC) represents a fundamental tool for protectingquantum information from noise and faulty operations [17],[18]. However, QEC operates by spreading the information ofone logical qubit into several physical qubits. Hence, solvingproblems of practical interest, such as integer factorization –which constitutes one of the most widely adopted algorithmsfor securing communications over the current Internet – ormolecule design may require millions of physical qubits [6],[7].

Hence, on one hand researchers worldwide are leveragingon the advancement of different technologies for qubit imple-mentation superconducting circuits, ion traps, quantum dots,and diamond vacancies among the others and innovative QECtechniques to scale the number of qubits beyond two-digits. Onthe other hand, the Quantum Internet, i.e., a network enablingquantum communications among remote quantum nodes, hasbeen recently proposed as the key strategy to significantly scaleup the number of qubits [19], [20], [1], [21], [22].

In fact, the availability of such a network and the adoptionof a distributed computing paradigm allows us to regard theQuantum Internet jointly as a virtual quantum computer witha number of qubits that scales linearly with the number ofinterconnected devices.

In this light, the aim of this paper is to provide thereader with an overview about the main challenges and openproblems arising with the design of a Distributed QuantumComputing ecosystem.

We start in Sec. II by introducing the Quantum Internet –as the fundamental underlying communication infrastructureof a Distributed Quantum Computing ecosystem – as well assome of its unique key applications. Then we go further inSec. III, by conceptualizing a high-level system abstractionof the Distributed Quantum Computing ecosystem from acommunication engineering perspective. Such an abstractionis described through a set of (logical) layers, with the higherdepending on the functionalities provided by the lower ones.Thereby, we clarify dependencies among the aforementionedlayers. Since, each layer of the ecosystem has some relatedopen challenges, within Sec. IV we survey such challengesand open problems. Finally, in Sec. V we conclude the paperwith some perspectives.

II. THE QUANTUM INTERNET

As mentioned in Sec. I, one promising approach to addressthe challenges arising with large-scale quantum processorrealization is to mimic modern high-performance computinginfrastructures – where thousands of processors, memoriesand storage units are inter-connected via a communicationnetwork, and the computational tasks are solved by adoptinga distributed approach.

To this aim, it is mandatory to design and deploy theQuantum Internet, which formally defines a global quantum

Fig. 1. Distributed Quantum Computing speed-up. The volume of cubesrepresents the ideal quantum computing power, i.e., in absence of noiseand errors. As evident by comparing the power available at isolated devicesversus the power achievable through clustered devices, the interconnectionof quantum processors via the Quantum Internet provides an exponentialcomputing speed-up with respect to isolated devices.

network2 able to transmit qubits and to distribute entangledquantum states3 among remote quantum devices [3], [1], [2],[19], [20], [21], [23].

In fact,the availability of the corresponding underlyingnetwork infrastructure and the adoption of the distributedquantum computing paradigm [25] allows us to regard theQuantum Internet – jointly – as a virtual quantum computerwith a number of qubits that scales linearly with the numberof interconnected devices. Hence, the Quantum Internet mayenable an exponential speed-up [26], [25], [1] of the quan-tum computing power with just a linear amount of physicalresources, represented by the interconnected quantum proces-sors. Indeed, by comparing the computing power achievablewith quantum devices working independently versus workingas a unique quantum cluster, the gap comes out - as depictedin Fig. 1 [1].

Specifically, increasing the number of isolated devices laysto a linear speed-up, with a double growth in computationalpower by doubling the number of devices. Conversely, increas-ing the number of clustered devices provides an exponentialgrowth, with a significant advantage clearly visible with justtwo interconnected devices. For instance, a single 10-qubitprocessor can represent 210 states thanks to the superpositionprinciple , hence two isolated 10-qubit processors can repre-sent 211 states. But if we interconnect the two processors,the resulting virtual device can represent up to 218 states

2 We refer the reader to [23], [24] for a discussion about the differencesunderlying the notion of “Quantum Internet” versus “quantum network”.

3The deepest difference between classical and quantum mechanics lays inthe concept of quantum entanglement, a sort of correlation with no counterpartin the classical world. For an in-depth introduction to quantum entanglementwe refer the reader to the classical book [17] , whereas a concise descriptioncan be found in [3].

[1], depending on the number of qubits devoted to fulfill thecommunication needs of the clustered processors as discussedin Sec. IV-B.

Before analyzing with further details in Sec. III the resultingDistributed Quantum Computing ecosystem from a communi-cation engineering perspective, it is worthwhile to note thatthe availability of the Quantum Internet infrastructure en-ables unparalleled capabilities not restricted to the distributedcomputing [21], [2]. Specifically, applications such as blindcomputing, secure communications and noiseless communi-cations have already been theorized or even experimentallyverified , as recently overviewed by an IETF Quantum InternetDraft [23].

Blind quantum computing [27], [28] refers to a server-clientarchitecture where clients can send sensitive data to server,which elaborates inputs without knowing their values. Thisfunctionality allows to achieve a twofold goal: preserving dataconfidentiality as well as solving tasks that are intractable forthe client – that can be a classical computer – but tractablefor the server, which implements the quantum paradigm.

Secure communications in the quantum field refers to theclass of communication protocols that exploit quantum me-chanics in order to get benefits unattainable using classicalInternet. For instance, in the field of quantum cryptography,researchers study strategies for sharing keys among partiesin total secrecy [29], [30], [31]. Whilst quantum byzantineagreement, a protocol used by multiple entities to distributivelyagree on a common decision, allows to achieve the consensusin a constant number of rounds, whereas classical protocolsscale polynomially with the number of processors [32].

Finally, the Quantum Internet provides the underlying in-frastructure to achieve transmission rates exceeding the fun-damental limits of conventional (quantum) Shannon theory[33], [34]. Specifically, by exploiting the capability of quantumparticles to propagate simultaneously among multiple space-time trajectories, quantum superpositions of noisy channelscan behave as perfect noiseless quantum communication chan-nels, even if no quantum information can be sent throughouteither of the noisy component channels individually [35].

III. DISTRIBUTED QUANTUM COMPUTING ECOSYSTEM

The overall aim of classical distributed computing is todeal with hard computational problems by splitting out thecomputational tasks among several classical devices , in orderto lighten the loads on single devices.

As mentioned in Sec. II, with the network infrastructure pro-vided by the Quantum Internet, this paradigm can be extendedto quantum computing as well: remote quantum devices cancommunicate and cooperate for solving computational tasksby adopting a distributed computing approach [26], [25]. Sincean entirely new paradigm – characterized by unconventionalphenomena ruled out by the quantum mechanics [1], such asno-cloning and entanglement – is involved, a new ecosystemneeds to be engineered.

The infographic in Fig. 2 is a stack depicting dependenciesamong a possible set of layers that together provide the

Local Operations

Virtual Quantum Processor

Quantum Processor

Quantum Link

ClassicalLink

Distributed Quantum Compiler

Distributed Quantum Algorithm

RemoteOperations

Fig. 2. A high-level system abstraction of the distributed quantum computingecosystem. The lowest layer provides the communication/network functionali-ties and consists of quantum processors interconnected with both classical andquantum links. Thanks to the underlying communication infrastructure, bothlocal and remote qubit operations can be executed. Hence, from a computingperspective, the two lowest levels concur to build a virtual quantum processorwith a number of qubits that scales with the number of inter-connectedphysical quantum processors. The virtual processor acts as an interface forthe distributed quantum compiler, which maps a quantum algorithm into asequence of local and remote operations , so that the available computingresources are optimized with respect to both the hardware and the networkconstraints.

Distributed Quantum Computing ecosystem. For the sake ofclarity, we restrict our attention to a network composed by twoquantum processors, directly inter-connected. Nevertheless,the discussion in the following can be easily extended to morecomplex network topologies, provided that end-to-end routingand network functionalities such as [36], [37], [38], [39], [40],[41] are available.

Starting from bottom, in Fig. 2 we have the communi-cation infrastructure underlying the Quantum Internet: spa-tially remote quantum devices able to communicate quantuminformation by means of a synergy of both classical andquantum communication resources. Indeed, as we overview inSec. IV-B, the transmission of quantum information generallyrequires the transmission of classical information as well,hence the availability of a classical network infrastructure –such as the classical Internet – is required [2], [3], [21]. Thisconstraint has been highlighted by interconnecting the twoquantum processors with both a classical and a quantum link.

By exploiting the communication functionalities providedby the lowest level, both local and remote qubit operations canbe executed. Specifically, the local operations – i.e., operationsbetween qubits stored within the same quantum processor –can be executed by exploiting the physical (or logical, whetherthe quantum device should natively implement QEC func-tionalities [42]) controls and readouts functionalities providedby the device. Conversely, the remote operations – i.e., the

q1 q2

q0

q3 q4 q5 q6 q8q7

q15 q14 q13 q12 q11 q9q10

Fig. 3. Coupling map of the ibmqx3 architecture: the nodes represent thequbits while the edges represent the possibility to have interactions betweentwo qubits, i.e., to implement the CNOT operation. As an instance, a CNOToperation can be directly executed between qubits q1 and q2 but not betweenqubits q1 and q3 .

CNOT

REVERSED CNOT SWAP

|ψq1〉 H H H H

|ψq2〉 H H H H

|ψq3〉

Fig. 4. A CNOT operation between non-adjacent qubits can be implementedthrough a sequence of swapping operations, with each swap consisting of threeCNOT (with the in-between CNOT being reverse, i.e., with target and controlqubits swapped) between adjacent qubits [46]. Thus, the circuit performs aCNOT between q1 and q3, leaving q2 unaltered. Note that H denotes theHadamard gate mapping a basis state into an even superposition of the basisstates [47], and that the quantum state stored within qubit qi is denoted –by adopting the standard bra-ket notation for describing quantum states – as|ψqi 〉.

operations between qubits stored at different quantum devices– pose further constraints, as discussed in Sec. IV.

Thanks to the abstraction provided by the two layers re-siding at the very bottom, a virtual quantum processor isobtained, where remote qubits are interconnected throughvirtual connections made possible by the remote operations.Clearly, remote operations are likely to be characterized bydelays and error rates notably larger than those characterizinglocal operations. Hence, local operations should be preferredover remote ones as much as possible, even though remoteoperations are unavoidable whenever the number of qubitsrequired to perform the computational task exceeds the numberof qubits available at a single device. Hence, an optimizationmust be performed by the distributed quantum compiler, sothat the different operations required by the quantum algorithmas well as the input to the algorithm itself are properlyallocated among the qubits of the different devices.

Finally, at the very top we have the quantum algorithm,which is completely independent and unaware of the phys-ical/logical constraints imposed by both the hardware andnetwork particulars, thanks to the abstraction provided by theunderlying levels. We can think at this module as a minimalservice for defining quantum algorithms, but also, in a widerperspective, as a platform where interesting functionalities areavailable - allowing, for instance, quantum machine learning[43] or quantum optimization algorithms [44], [45].

However, several complications have been omitted so far. In-deed, communication protocols intrinsically imply overhead ,i.e., computing resources need to be dedicated, in order to dealwith transmission processes and errors correction. Therefore,it’s worth going further towards this discussion, expanding

components of the proposed ecosystem and considering openchallenges related with.

IV. OPEN CHALLENGES AHEAD

The aim of this section is to describe and to discuss some ofthe open problems related with the proposed Distributed Quan-tum Computing ecosystem. For this, some layers are individu-ally discussed. Specifically, in Sec. IV-A quantum processorsare considered, paying particular attention to drawbacks in-duced by local operations involving multiple qubits. Sec. IV-Bintroduces the interconnection between remote quantum pro-cessors, discussing the quantum teleportation as a mean totransfer quantum information between interconnected devices.After that, in Sec. IV-C we discuss the gate teleportation as astrategy to perform remote operations. Sec. IV-D describes thelayer responsible for abstracting and optimizing the executionof the quantum algorithms, based on the characteristics of theunderlying system. Finally, in Sec. IV-D we discuss some ofthe current standardization efforts.

A. Quantum ProcessorThe most basic element of a distributed quantum computing

ecosystem is identifiable with the local quantum computingdevice. Here the qubits are connected according to somedirected and connected graph – namely, the coupling map– that accounts for the hardware limitations resulting fromcontrolling and preserving the quantum information fromdecoherence and noise. As an example, Fig. 3 depicts thecoupling map of the ibmqx3 quantum processor [46], withnodes representing qubits while edges represent the possibilityto have interactions between two qubits, i.e., to implement oneof the fundamental quantum operations: the CNOT operation4.In fact, there exists a universal quantum gate set5 with CNOTas the only operator belonging the set that involves more thanone qubit. Thus, we can focus on problems related to the CNOToperation keeping the discourse general.

It is immediate to observe that only nodes – i.e., qubits –linked by an edge can directly interact [49]. Nevertheless,

for an algorithm designer it is crucial being able to define acircuit without restrictions on interactions. Indeed, a circuitprogramming model can easily abstract from this restriction[17], resulting in a fully connected graph at the cost of anoverhead due to indirect execution of the desired operation.For instance, let us consider to carry out a CNOT between thetwo non-adjacent qubits q1 and q3 of Fig. 3. By performingtwo state swapping operations for each edge belonging to theshortest-path from node q1 towards node q3, the overall resultwill be equivalent to a CNOT between q1 and q3, keeping otherstates unchanged. Fig. 4 clarifies the process above.

The overhead induced by the swapping operations explainshow important is the topological organization of devices andthe circuit design as well.

4The CNOT operation involves two qubits, referred to as control qubit andtarget qubit. It works as follows [47]: if the control qubit is 1, then the targetqubit value is flipped. Otherwise, nothing happens.

5 A universal gate set is any set of gates which any operation possible ona quantum computer can be reduced to [48].

ION TRAP

SUPERCONDUCTING QUBITS

SATELLITE-FREESPACE CHANNEL

GROUND-FREESPACE CHANNEL

OPTICALFIBER CHANNEL

QUANTUM DOTS

Fig. 5. Pictorial representation of a matter-flying transducer, which is neededto convert matter qubits – i.e., qubits for information processing/storing – intoflying qubits – i.e., qubits for information transmission – and vice versa.

B. Quantum Link

As mentioned in Sec. III, the Quantum Internet requiresboth classical and quantum links. In this perspective, a distinc-tion between matter and flying qubits – i.e., between qubitsfor information processing/storing and qubits for informationtransmission – must be made [2].

As regards to the matter qubits, several candidate technolo-gies are available, each one with its pros and cons [25]. Con-versely, as regards to the flying qubits, there exists a generalconsensus about the adoption of photons as qubit substrate[2]. However, heterogeneity arises by considering the differentphysical channels the photons propagate through, ranging fromfree-space optical channels (either ground or satellite free-space) to optical fibers. Thus, a transducer for matter-flyingconversion is needed as depicted in Fig. 5 and discussed withfurther details in [2]. And communication models need to takeinto account such a technological heterogeneity , with the aimof providing a black box for upper protocol layers with onecommon logic.

Furthermore, quantum mechanics does not allow an un-known qubit to be copied or even simply observed/measured.As a consequence, the communication techniques utilizedto interconnect spatially remote quantum devices cannot bedirectly borrowed from classical communications. In this con-text, quantum teleportation is widely accepted as one of themost promising quantum communication technique betweenremote quantum nodes [51], [52], [3]. Quantum teleportationhas been experimentally verified [53] and it requires, asdepicted in Fig. 6, a pair of parallel resources6. One of these

6 For an in-depth discussion about the quantum teleportation process , werefer the readers to [3].

SOURCE

DESTINATION

|ψ〉 H

|Φ+〉X Z |ψ〉

Fig. 6. Quantum teleportation circuit. First two wires belong to source,whereas the bottom wire belongs to destination. A generic state |ψ〉 is initiallystored at the source . Once the teleportation process is fulfilled, the originalstate is available at the destination, regardless of its value. |Φ+〉 represents anEPR pair, that is a couple of maximally entangled qubits [50]. The result ofthe measurement process at the source is sent to the destination via a classicallink . The carried classical bits are thus used for determining whether gatesX and Z – corresponding to a bit- and a phase-flip, respectively [47] – mustbe performed or not, in order to recover the original state |ψ〉 from the EPRpair member available at the destination.

resources is classical: two bits must be transmitted from thesource to the destination. The other resource is quantum: anentangled pair of qubits must be generated and shared betweenthe source and the destination.

In the context of the distributed quantum computing ecosys-tem, quantum teleportation constitutes the foundation of acommunication paradigm known as teledata [54], which gen-eralizes the concept of moving state among qubits to remotedevices.

To provide a concrete example of the teledata concept,a further distinction must be made between communicationqubits and data qubits. Specifically, within each quantumdevice, a subset of matter qubits is reserved for fulfilling thecommunication needs to generate entanglement. These qubitsare called communication qubits [23], to distinguish themfrom the remaining matter qubits within the device devotedto processing/storage, referred to as data qubits.

As an example, consider two ibmqx2 architectures [55]interconnected via quantum teleportation as depicted in Fig. 7.The c0, c1 pair is in the state |Φ+〉 - that is the standard notationto denote a couple of maximally entangled qubits [17], alsoknown as EPR pair [50]. Any kind of interaction betweenremote devices involves communication qubits, but not all thedata qubits are connected with them. As already explainedin Sec. IV-A, interactions between non-adjacent qubits arefeasible but they imply an overhead. A solution would beadding more qubits to the communication set, but it meanssacrifice further valuable resources for processing and storage.For this reason, the selection of the communication qubit setis a crucial task within the distributed quantum computingecosystem and it implies a carefully evaluation of the trade-off between the number of data and communication qubits.

Next section shows how to exploit teleportation in order tonot only send information but also perform joint operationsbetween remote qubits.

q0

c0q1q2

q3

c1

q4

q5

q6

q7|Φ+〉

Fig. 7. Coupling map representing physical architecture of two quantumdevices ibmqx2 interconnected via the quantum teleportation paradigm.Nodes labeled with c0 and c1 denote communication qubits, and the dottedline indicates that they are in the entangled state |Φ+〉, i.e., they form an EPRpair. Conversely, qi with i ∈ {0, 1, 2, 3} denote data qubits – i.e., qubitsavailable for computing tasks.

C. Teleporting Gates

Distributed quantum computation requires the capability toperform quantum operations on qubits belonging to remotequantum devices.

As mentioned in the previous section, one possible solutionis to resort to the teledata concept, by moving the quantuminformation from a quantum device to another via the telepor-tation process, through an entangled pair.

However, an entangled pair allows one to implement also aso-called teleporting gate, or telegate [56]. From a theoreticalperspective, we have already observed that providing the CNOToperation - together with other single qubit gates - is enough toperform any kind of quantum algorithm. Therefore, returningto stack dependencies of Fig. 2, we can conceptualize aservice that provides a set of remote operations based onteleported gates. Such service will directly interact with thephysical system, exploiting the entanglement generation anddistribution functionality [3].

Specifically, by considering the topology depicted in Fig. 7,it is possible to implement the CNOT as the joint operationbetween qubits belonging to spatially remote devices. Indeed,by exploiting the availability of two communication qubits– c0 and c1 – shared between the two remote devices andstoring an EPR pair, it is possible to perform a remote CNOToperation7 with, for example, q0 as control qubit and q4 astarget qubit. Fig. 8 shows the corresponding circuit, consistingof local CNOT operations and single-qubit operations andmeasurements.

D. Distributed Quantum Compiler

Concepts discussed so far provide some fundamental under-lying communication functionalities enabling the distributedquantum computing paradigm.

Indeed, the definition of a quantum algorithm can be veryabstract. In general, it goes through the definition of a quantumcircuit – where a computation is a sequence of quantum gateson a register – as those depicted in Figs. 6 and 8. And

7 For a more comprehensive presentation of the telegate, we refer the readerto [57].

SOURCE

DESTINATION

|ψ〉 Z

|Φ+〉

H

|φ〉 X

Fig. 8. Quantum telegate circuit implementing a CNOT operation betweenremote qubits. Specifically, a CNOT operation between qubits placed atdifferent devices – say qubits q0 and q4 in Fig. 7– is performed throughCNOTs between each qubit and the member of an EPR pair stored at thesame device, followed by single-qubit gates and measurements. Note that |ψ〉and |φ〉 denote the generic initial states stored at q0 and q4, respectively,whereas |Φ+〉 denotes the EPR pair stored by the communications qubits –say qubits c0 and c1 in Fig. 7.

algorithm designers may benefit from an abstraction whichhides the complications due to physical features.

However, as mentioned in Sec. III, within the Virtual Quan-tum Processor remote qubits belonging to remote quantumdevices are interconnected through virtual connections madepossible by the remote operations as described in Secs. IV-Band IV-C. Unfortunately, remote operations are likely to becharacterized by delays and error rates larger than localoperations. The reason underlying this statement is that eachprotocol step needed for realizing remote operations – from theentanglement distribution to the gate operations – is affectedby decoherence [3], i.e., by a quantum-specific noise process.Decoherence affects local operations as well. However, sincethe effects of such a noise become stronger as function ofthe time [3], [2], remote operations, by involving furtheraway parties, are more vulnerable. It follows that, given aparticular quantum circuit describing a quantum algorithm,the Distributed Quantum Compiler is required to optimize thecircuit8 so that the number of remote operations is minimizedas much as possible to limit the decoherence effects.

Furthermore, the compiler should be able to optimize thecircuit so that it can be executed regardless of the underlyingnetwork topology. Indeed, it may be the case that two remotequantum devices are not directly connected – i.e., no com-munication qubits are shared between the two devices – eventhough some remote operations between qubits stored at thesedevices are required. Hence, the compiler should optimizethe corresponding quantum circuit so that the entanglementswapping operations9 among remote devices are minimized.Finally, as discussed in Sec. IV-B, there exists a trade-off

8 Note that a circuit optimization is needed also in case of a single quantumprocessor [46], [58] to reduce the overhead arising with the swap operationsdiscussed in Sec. IV-A.

9 Entanglement swapping is a technique used to entangle distant nodes –without physically sending an entangled qubit through the entire distance –by swapping the entanglement generated at intermediate nodes [52].

between data and communication qubits. The larger is thenumber of communication qubits in a device, the higher is therate of remote operations achievable at the price of reducingthe number of qubits devoted to computation.

E. What’s Next

Considering modern available technologies, it seems reason-able to envision that we will see a first attempt of interconnec-tion among quantum computers located nearby. Likely, one ofthe main tech companies currently providing cloud access toisolated quantum computers – such as IBM [59], HIQ [60],Amazon Braket [61] or Azure Quantum [62] – will scalethe available quantum computing power by interconnectingfew quantum computers located few meters away within aquantum farm [2], [4]. After that, consider that some of thesecompanies will have quantum computers distributed over theworld. Thus, it would not be surprising to see interconnectionamong quantum computers or even among quantum clustersmiles away from each other.

However, interconnecting quantum devices implies the needfor a communication standard. In other words, remote devices– likely to have technological differences – will need toagree on network protocols in order to exchange interpretableinformation. Thus, the Quantum Internet will need a logicalarchitecture as well as the classical Internet does – i.e., withthe TCP/IP Internet protocol suite being the standard de-facto. Research in this direction has already started, withinthe Internet Engineering Task Force (IETF), where researchersare trying to conceptualize the Quantum Internet as a service-oriented platform [24], [23].

V. CONCLUSIONS

With this paper, we have presented a layered ecosystem thatoutlines a possible key strategy towards large-scale quantumprocessor design based on the distributed quantum computingparadigm. Within the envisioned ecosystem, the lowest layersintegrate the Quantum Internet as the fundamental underlyinginfrastructure providing networking and communication func-tionalities among remote quantum devices. Conversely, the up-per layers are responsible for mapping the quantum algorithmonto the underlying physical infrastructure by optimizing theavailable computational resources as well as by accounting forthe constraints induced by the hardware/network configuration.

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