DQC2O Distributed Quantum Computing for Collaborative Optimization in Future Networks Napat Ngoenriang Minrui Xu Jiawen Kang Dusit Niyato Han Yu and Xuemin Sherman Shen

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DQC2O: Distributed Quantum Computing for

Collaborative Optimization in Future Networks

Napat Ngoenriang, Minrui Xu, Jiawen Kang, Dusit Niyato, Han Yu, and Xuemin (Sherman) Shen

Abstract—With the advantages of high-speed parallel pro-

cessing, quantum computers can efﬁciently solve large-scale

complex optimization problems in future networks. However,

due to the uncertain qubit ﬁdelity and quantum channel noise,

distributed quantum computing which relies on quantum net-

works connected through entanglement faces a lot of challenges

for exchanging information across quantum computers. In this

paper, we propose an adaptive distributed quantum computing

approach to manage quantum computers and quantum channels

for solving optimization tasks in future networks. Firstly, we

describe the fundamentals of quantum computing and its dis-

tributed concept in quantum networks. Secondly, to address the

uncertainty of future demands of collaborative optimization tasks

and instability over quantum networks, we propose a quantum

resource allocation scheme based on stochastic programming for

minimizing quantum resource consumption. Finally, based on

the proposed approach, we discuss the potential applications

for collaborative optimization in future networks, such as smart

grid management, IoT cooperation, and UAV trajectory plan-

ning. Promising research directions that can lead to the design

and implementation of future distributed quantum computing

frameworks are also highlighted.

Index Terms—Distributed quantum computing, quantum net-

works, resource allocation

I. INTRODUCTION

In the quantum era, the advancement of quantum computing

and communication has attracted signiﬁcant interest from

researchers, government organizations and the industry [1].

Quantum computers provide effective solutions to complex

optimization problems in a resource efﬁcient manner, a feat not

possible for classical computers to achieve. The recent adop-

tion of quantum computing has further boosted technology in-

novations such as artiﬁcial intelligence (AI), intelligent trafﬁc

monitoring, weather forecasting, improved battery chemistry,

and life-saving pharmaceuticals [1]. The proliferation of quan-

tum computing has also evolved to accelerate computation for

various applications and services in future networks, which

must be designed efﬁciently using limited resources to perform

a wide range of heterogeneous tasks [2].

N. Ngoenriang is with the School of Information Science and Technol-

ogy, Vidyasirimedhi Institute of Science and Technology, Thailand (e-mail:

naphat.n s17@vistec.ac.th.

M. Xu, H. Yu and D. Niyato are with the School of Computer Science

and Engineering, Nanyang Technological University, Singapore (e-mail: min-

rui001@e.ntu.edu.sg; han.yu@ntu.edu.sg); dniyato@ntu.edu.sg).

J. Kang is with the School of Automation, Guangdong University of

Technology, China (e-mail: e-mail: kavinkang@gdut.edu.cn.

X. (Sherman) Shen is with the Department of Electrical and Computer

Engineering, University of Waterloo, Waterloo, ON, Canada, N2L 3G1 (e-

mail: sshen@uwaterloo.ca).

The principles of quantum mechanics are used to enable

quantum bits (i.e., qubits) in quantum computers which are

superior to classical computers based on binary bits. For

example, Shor’s [3] algorithm and Grover’s [4] algorithm,

two well-known quantum algorithms, were developed to ef-

ﬁciently solve factorization and search for unstructured data,

respectively, These tasks are highly challenging for classical

computers. However, scaling up quantum computers is a key

challenge in deploying quantum computers in practice. To

date, only a small number of qubits can be implemented

in a single quantum computer. Moreover, quantum tasks

usually require the use of multiple qubits in more complex

applications. Due to the instability of qubits and the amount

of information required, it becomes more difﬁcult to manage

and control information in quantum computers with a small

number of qubits. Thus, distributed quantum computing has

been proposed in an attempt to alleviate this problem [5].

The concept of distributed quantum computing, which refers

to multiple interconnected quantum computers, was introduced

to accelerate and perform collaboratively quantum computa-

tions through quantum networks. However, due to the prin-

ciples of quantum mechanics, qubits cannot be duplicated or

cloned. Distributed quantum computing requires quantum tele-

portation, in which qubits are teleported between two quantum

computers. In this way, a large, complex computational task

can be accomplished jointly by multiple quantum computers.

It has been shown that the most commonly used quantum

algorithms beneﬁt from their distributed counterparts. For

example, distributed Grover’s algorithm [4] incurs signiﬁcantly

shorter query time than Grover’s algorithm, and distributed

Shor’s algorithm [3] is less complex than Shor’s algorithm.

The distributed versions of both algorithms increase their

viability of solving complex problems in practice.

Although distributed quantum computing has many advan-

tages over a single quantum computer and classical computers,

designing efﬁcient large-scale distributed quantum comput-

ing still faces many challenges. Firstly, the effectiveness of

using quantum computers is determined by the demand of

the applications, like military communication. This is un-

known at the time of deployment, making planning difﬁcult.

Secondly, the availability and computing power of quantum

computers, which may vary over time, also affects whether

quantum tasks can be fully computed. Thirdly, distributed

quantum computing may suffer from ﬁdelity degradation. This

is unavoidable at the moment, and reduces the efﬁciency of

quantum teleportation in quantum networks. Thus, deploying

arXiv:2210.02887v1 [cs.DC] 16 Sep 2022

Quantum computer

operator

Provision of the deployed

quantum computers

Provision of on-demand

quantum computer deployment

Applications require the

use of quantum computing

Minimize costs of using the

deployed quantum computers

under quantum resources

Perform quantum computing on

distributed quantum computing

Smart Grid

Internet of Things

Entanglement

Superposition

Properties of quantum mechanics

Measurement/Interference

Military

Fig. 1: The adaptive resource allocation approach with two-stage stochastic programming for distributed quantum computing.

quantum resources in distributed quantum computing in its

current form may result in highly inefﬁcient utilization of

quantum computing resources due to the inherent uncertainty

in real-world circumstances.

To address the above challenges, in this paper, we propose

an adaptive resource allocation approach towards efﬁcient

and scalable distributed collaborative quantum computing. It

consists of deterministic and stochastic programming models

for quantum resource allocation with uncertainty in collabo-

rative settings to help quantum computer operators minimize

total deployment costs. It jointly considers the uncertainty of

future quantum computing demands, the computing power of

quantum computers, and the ﬁdelity in distributed quantum

computing in order to optimally deploy and utilize quantum

computers. We conduct extensive experiments to reveal the

importance of the optimal deployment of quantum computers

in distributed quantum computing. In comparison to other

resource allocation models, the proposed approach can reach

the lowest total deployment cost. Finally, we highlight oppor-

tunities and challenges in distributed quantum computing for

various military applications in future networks.

II. FUNDAMENTALS OF QUANTUM COMPUTING

A. Quantum Computing

Three properties of quantum mechanics deﬁne quantum

computing: superposition, interference, and entanglement, as

shown in Fig. 1.

1) Superposition: In classical computers, the binary bits

0 and 1 are used to encode information for computations.

A superposition in quantum computing allows the encoding

of qubits in a combination of two classical binary states. A

well-known example of quantum mechanics is the tossing of

a coin. When a coin is tossed in the air, the exact outcome is

unknown, and its probability values reﬂect qubits. Each qubit

can be expressed as a linear combination of binary states,

where the coefﬁcients correspond to the probabilities of the

qubit amplitudes. Due to the superposition, nqubits can store

2npossible outcomes and have the same chance of being

measured for each. Therefore, quantum computers can store

and manipulate more information than classical computers,

providing far more diverse possibilities and opportunities.

2) Interference: Qubits must be subjected to some kind

of measurement in order to represent and store their values

and results. If one intervenes in the process, it is possible to

measure and see the results of the paths. When the process is

interrupted, the states of the qubits collapse to classical bits,

and the computation results appear. For example, the result of

a coin toss is known deﬁnitively (e.g., heads or tails) when

the coin reaches the bottom.

3) Entanglement: Two qubits can be entangled with each

other as an entanglement pair [5], which means that when one

qubit is measured, the other qubit can also be known because

of their entangled nature. In addition, a pair of entanglement

qubits is entangled maximally also known as a Bell state when

the results of measuring one of them will certainly affect

the outcome of measuring the other one later. The ﬁdelity

of entanglement pairs is the metric of attenuation for the

entangled qubits between two remote quantum computers. The

ﬁdelity scale runs from 0 to 1, where 1 indicates the best

performance that the entanglement can achieve.

The main analogies between classical computing and the

technology used to realize a true quantum computer are the

following. In classical computing, a circuit is a computational

model that enables the processing of input values through

gates and operations. Similarly, the quantum circuit model

proceeds with implementations on qubits and involves an

ordered sequence of quantum gates that permit logical in-

teraction between qubits. In particular, the measurement of

qubits must occur near the end of the quantum circuit. A

quantum processor is a small quantum computer that can

execute quantum gates on a small number of qubits and allows

the entanglement of qubits inside.

B. Distributed Quantum Computing

The concept of distributed quantum computing relies on the

following principles:

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DQC2O:DistributedQuantumComputingforCollaborativeOptimizationinFutureNetworksNapatNgoenriang,MinruiXu,JiawenKang,DusitNiyato,HanYu,andXuemin(Sherman)ShenAbstractWiththeadvantagesofhigh-speedparallelpro-cessing,quantumcomputerscanefcientlysolvelarge-scalecomplexoptimizationproblemsinfuturenetworks....

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DQC2O Distributed Quantum Computing for Collaborative Optimization in Future Networks Napat Ngoenriang Minrui Xu Jiawen Kang Dusit Niyato Han Yu and Xuemin Sherman Shen

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