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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 |
2202 |
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 |
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