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Optimal Stochastic Resource Allocation for
Distributed Quantum Computing
Napat Ngoenriang∗, Minrui Xu†, Sucha Supittayapornpong∗, Dusit Niyato†, Han Yu†, Xuemin (Sherman) Shen‡
∗School of Information Science and Technology, Vidyasirimedhi Institute of Science and Technology, Thailand
†School of Computer Science and Engineering, Nanyang Technological University, Singapore
‡Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada
Abstract—With the advent of interconnected quantum com- (i.e., qubits). A qubit offers more information storage and
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puters, i.e., distributed quantum computing (DQC), multiple computation choices than binary bits in classical computers.
quantum computers can now collaborate via quantum networks
In quantum mechanics, entanglement describes a correlation
to perform massively complex computational tasks. However,
between two qubits in which the values of one qubit may
DQC faces problems sharing quantum information because it
peS cannot be cloned or duplicated between quantum computers. depend on another. To observe the values of qubits, measure-
Thanks to advanced quantum mechanics, quantum computers ment,oftenreferredtoasinterference,canbeusedtointerrupt
can teleport quantum information across quantum networks. the processing of quantum computers.
However, challenges to utilizing efficiently quantum resources,
61 Quantum algorithms enable qubits in quantum computers
e.g., quantum computers and quantum channels, arise in DQC
by utilizing quantum mechanics. For instance, Shor’s [6]
due to their capabilities and properties, such as uncertain qubit
fidelity and quantum channel noise. In this paper, we propose and Grover’s [7] algorithms were developed to deal with
]CD.sc[
a resource allocation scheme for DQC based on stochastic pro- factorizationandthesearchforunstructureddata,respectively,
grammingtominimizethetotaldeploymentcostforquantumre- whicharehighlychallengingforclassicalcomputers.Totackle
sources.Essentially,thetwo-stagestochasticprogrammingmodel these tasks with quantum computers, at least the order of 106
is formulated to handle the uncertainty of quantum computing
physical qubits are required [6]. However, a recently devel-
demands, computing power, and fidelity in quantum networks.
The performance evaluation demonstrates the effectiveness and oped quantum computer can only contain tens of qubits [8].
ability of the proposed scheme to balance the utilization of Therefore, it becomes increasingly challenging to handle and
1v68820.0122:viXra quantum computers and on-demand quantum computers while control information in quantum computers due to the limited
minimizing the overall cost of provisioning under uncertainty.
number of qubits, the instability of qubits, and the amount of
Index Terms—Distributed Quantum Computing, Quantum
information required for complex computational tasks. As a
Networks, Resource Allocation, Stochastic Programming
result, the concept of DQC has been presented.
In DQC, quantum teleportation, or the transfer of qubits, is
I. INTRODUCTION
required for quantum computers to connect and collaborate.
To date, quantum computing is tremendously fast and effi- In this regard, multiple quantum computers can work col-
cient, being able to do computations in a matter of seconds laboratively to compute a large-scale complex computational
which would take decades for older supercomputers [1]. In task at quadratic or exponential speed-up. Moreover, most of
2019, a prototype of Google’s quantum computer was able to commonquantumalgorithmscanbenefitfromtheirdistributed
finish the computation and demonstrate the effectiveness of equivalents. For example, distributed Shor’s algorithm can
quantum mechanics [2]. Breakthroughs in quantum comput- reduce computational complexity compared to original Shor’s
ing are essential and influence various applications, such as algorithm[9].Additionally,distributedGrover’salgorithmhas
artificial intelligence (AI), molecular modelling, weather fore- aconsiderablylowerquerytimethanGrover’salgorithm[10].
casting, and drug development [3]. Since the development of Therefore, distributed quantum algorithms can enhance prac-
quantum computers is still in its infancy, distributed quantum tical feasibility of quantum computers in tackling complex
computing (DQC) has emerged in significance to solve more computational tasks in practice.
complex computational tasks. In the next quantum computing Although DQC and distributed quantum algorithms have
era,IBM[4]andGoogle[5]aimtointroduceapracticalDQC, evolved and accelerated to handle complex computational
whichisanticipatedin2025.AlthoughtheadventofDQChas tasks, quantum resources, e.g., quantum computers and quan-
alsoadvancedprocessingspeedforavarietyofheterogeneous tum channels, must be optimally allocated to perform hetero-
tasks, quantum resources are still limited and need to be geneouscomputationaltasks.However,theefficientutilization
managed effectively while performing computations. of quantum resources in DQC is still facing challenges.
The basis for the development of quantum computing is First, the utilization of quantum resources depends on the
formedbasedonpropertiesofquantummechanics,i.e.,super- demands of computational tasks, which are not known pre-
position, entanglement, and interference, as shown in Fig. 1. cisely at the time of quantum computer deployment. Second,
Superposition permits encoding in a mixture of two states quantum computers’ availability and computing power may
Provision of the deployed
Entanglement quantum computers
Superposition
Measurement/Interference
Properties of quantum mechanics Minimize the total
deployment cost
Quantum
computer operator
Provision of on-demand Perform distributed
Computational Tasks
quantum computers quantum computing
Fig. 1: The illustration of system model of distributed quantum computing.
or may not be available to compute computational tasks. which gives a quadratic computing speed-up [7] to search op-
Third, fidelity degradation occurs when performing quantum erationsinnon-structuredatabases.Thesequantumalgorithms
teleportation and transferring qubits over quantum networks, canbeadoptedtooutperformexistingconventionalalgorithms
whichdegradestheefficacyoftheentangledqubits.Duetothe with quadratic or exponential speed-up computations [13].
uncertainty, allocating quantum resources in DQC may result However, due to challenges in scaling up the number
in both under and over-deployment of quantum computers. of qubits, quantum computers are not yet ready to replace
In addition, because of the limitations of quantum resources, traditionalcomputers[14].Therefore,DQCwasintroducedto
quantum computers can be purchased or outsourced from combine several quantum computers to handle more complex
other organizations such as Amazon Braket [11] to complete computational tasks [14], [15]. Most existing works look at
complexcomputationaltasks.However,thecostofon-demand distributed quantum mechanics and algorithms to be the basis
quantum computers is relatively more expensive. in DQC [14], [15]. Similar to quantum algorithms, distributed
Toaddresstheaforementionedchallenges,inthispaper,we Shor’s[9]andGrover’s[10]algorithmswerewidelyused.The
proposearesourceallocationschemebasedonstochasticpro- distributed Shor’s algorithm has a computing complexity of
gramming to minimize the total deployment cost to compute O((logN)2),whichoutperformstheoriginalShor’salgorithm,
computational tasks in DQC. The main contributions of this i.e., O((logN)2log(logN)log(log(logN))), where N is the
paper can be summarized as follows: numbertobefactored[9].Grover’salgorithmincursexpensive
query time due to its use of superpositions as inputs. Accord-
• We propose an optimal resource allocation scheme to
ing to [9], the distributed Grover’s algorithm was devised to
compute computational tasks in DQC. In particular, the
improvetheo √riginalGr√over’salgorithmbyreducingthequery
optimalresourceallocationarejointlyobtainedunderthe
timesfrom π 2n to π 2n−k,wherenisthenumberofinput
uncertainties of future demands of computational tasks 4 4