text stringlengths 0 8.13M |
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6 7 8 9 10 11 99 106 113 120 127 134 141 148 0.0 0.25 0.5 0.75 1.0 |
The number of required qubits The computing power of QC (Qubits) The fidelity of the Bell pairs |
Fig. 3: Cost breakdown under differentFig.4:Coststructureunderdifferentcom-Fig. 5: Cost breakdown under different |
demands of the computational task. puting power of the quantum computer. fidelity of the Bell pairs. |
1e4 1e4 1e5 |
8 T Do et pa .l QC Cos Ct ost 8 T Do et pa .l QC Cos Ct ost 1.6 Proposed model |
Comp. Cost Comp. Cost EVF model |
6 C Oo nm -dm em. C ao ns dt QC Cost 6 C Oo nm -dm em. C ao ns dt QC Cost 1.4 Random model |
1.2 |
latoT 4 latoT 4 latoT |
1.0 |
0.8 |
2 2 |
0.6 |
0 0 |
1x cost 2x cost 3x cost 4x cost 5x cost 0.0 0.2 0.4 0.6 0.8 1.0 1x cost 2x cost 3x cost 4x cost 5x cost |
Cost of on-demand QC Probability of the scenario ( 1) Cost of on-demand QC |
Fig.6:Costbreakdownunderdifferenton-Fig. 7: Cost breakdown under differentFig. 8: Cost comparison among the pro- |
demand QC costs. probabilities. posed, EVF, and random models. |
pairs for the shared entangled qubits to be 5000, 1000, and computationaltasksequals11,on-demandquantumcom- |
450,respectively,basedon[25].AllBellpairsamongquantum puters must be deployed to compute the computational |
computers have identical costs and qubit capacities, i.e., 257 task, as it exceeds the computing power of the currently |
qubits.Thecostandcomputingpowerofon-demandquantum deployed quantum computers. |
computers are 25000 and 127, respectively. In the stochastic ii) Wevarythecomputingpower(i.e.,thenumberofqubits) |
model, we consider two scenarios, i.e., |Ω| = 2. The first of quantum computers. For ease of presentation, all |
scenario is ω in which the demand of the computational task quantum computers are identical. The cost structure, i.e., |
1 |
is 10, the computing power of the quantum computers is 127 the first-stage, second-stage, and total deployment costs, |
qubits, and the fidelity of the Bell pairs is 1 (i.e., the best is shown in Figure 4. As the computing power increases, |
performance). The second scenario is ω in which there is weseethattotaldeploymentcostsarefalling.Toachieve |
2 |
nodemandforthecomputationaltask,allquantumcomputers thelowesttotalcost,thereisatrade-offbetweenthefirst- |
havenoavailablecomputingpower,andthefidelityoftheBell stagecosttousethedeployedquantumcomputersandthe |
pairsis0(i.e.,theworstperformance).Weassumethedefault second-stag cost to use on-demand quantum computers. |
probability values with π(ω ) = 0.8 and π(ω )=0.2. iii) We vary the fidelity of the entangled qubits in DQC |
1 2 |
We conduct experiments via GAMS script, which can be from 0 to 1. To simplify the evaluation, all the Bell |
solved by MINLP solver [27]. Some parameters are varied in pairs are identical. The results are shown in Fig. 5. |
different experiments. When the fidelity of the Bell pairs is less than 0.5, on- |
demandquantumcomputerdeploymentsarenecessaryas |
B. Impact of Demands, Computing Power, and Fidelity |
the entanglement of the qubits cannot be achieved. The |
In these experiments, we consider three important factors: computational tasks can be computed completely when |
i) the demand of the computational task, ii) the computing the fidelity of the entangled qubits is equal to or greater |
power of quantum computers, and iii) the fidelity of the Bell than 0.5. |
pairs across quantum computers. |
C. Impact of Cost of On-Demand Quantum Computers |
i) We vary the demand of the computational task from 6 to |
11 qubits. Fig. 3 demonstrates the cost breakdown. The We observe the total deployment cost of the proposed |
quantity of deployed quantum computers also increases schemebyvaryingthecostofon-demandquantumcomputers. |
as the demand rises. Moreover, when the demand for The cost breakdown is shown in Fig. 6. When the cost of an |
on-demand quantum computer equals to, or less than 2x, both [3] “10 Quantum Computing Applications and Examples.” https://builtin. |
the deployed quantum computers and on-demand quantum com/hardware/quantum-computing-applications. |
[4] “Expanding the IBM Quantum roadmap to anticipate the future |
computers are used. The cost of using the deployed quantum |
of quantum-centric supercomputing,” https://research.ibm.com/blog/ |
computer is lower than those of using on-demand quantum ibm-quantum-roadmap-2025,accessed:2022-08-25. |
computers when the on-demand quantum computer is more [5] “Google In Quantum: How The Tech Giant Is Competing For |
The Next Era Of Computing,” https://www.cbinsights.com/research/ |
expensive,i.e.,higherthan2x.Moreover,theproposedscheme |
google-big-tech-quantum/,accessed:2022-08-25. |
canadapttheutilizationofquantumcomputersandon-demand [6] P. W. Shor, “Polynomial-time algorithms for prime factorization and |
quantum computers to minimize the total deployment cost discretelogarithmsonaquantumcomputer,”SIAMreview,vol.41,no.2, |
pp.303–332,1999. |
despite the variations in on-demand quantum computer costs. |
[7] L. K. Grover, “Quantum mechanics helps in searching for a needle in |
ahaystack,”Physicalreviewletters,vol.79,no.2,p.325,1997. |
D. Impact of Probability of Scenarios |
[8] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, |
We vary the probability of the scenario ω , which cor- R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell et al., “Quantum |
1 supremacy using a programmable superconducting processor,” Nature, |
responds to having the demand of the computational task, |
vol.574,no.7779,pp.505–510,2019. |
the computing power, and the positive performance of the [9] A. Yimsiriwattana and S. J. Lomonaco Jr, “Distributed quantum com- |
entangled qubits. The cost breakdown is shown in Fig. 7. We puting: A distributed shor algorithm,” in Quantum Information and |
ComputationII,vol.5436. SPIE,2004,pp.360–372. |
observe that when the probability of the scenario is equal to |
[10] D. Qiu and L. Luo, “Distributed grover’s algorithm,” arXiv preprint |
orlessthan0.2,theon-demandquantumcomputerisrequired arXiv:2204.10487,2022. |
due to a small amount of demand. The proposed scheme [11] “Amazon Braket,” https://aws.amazon.com/braket/, accessed: 2022-08- |
25. |
suggests using the deployed quantum computers instead of |
[12] A. Steane, “Quantum computing,” Reports on Progress in Physics, |
on-demand quantum computers when the probability of the vol. 61, no. 2, pp. 117–173, feb 1998. [Online]. Available: |
demand, the computing power, and the fidelity increase. https://doi.org/10.1088/0034-4885/61/2/002 |
[13] G.Raj,D.Singh,andA.Madaan,“Analysisofclassicalandquantum |
E. Cost Comparison computing based on grover and shor algorithm,” in Smart Computing |
andInformatics. Springer,2018,pp.413–423. |
We compare the total deployment cost of the proposed [14] S.Wehner,D.Elkouss,andR.Hanson,“Quantuminternet:Avisionfor |
theroadahead,”Science,vol.362,no.6412,p.eaam9288,2018. |
stochastic model with the random model and the Expected |
[15] A.S.Cacciapuoti,M.Caleffi,F.Tafuri,F.S.Cataliotti,S.Gherardini, |
Value Formulation (EVF) model. The EVF model solves the andG.Bianchi,“Quantuminternet:Networkingchallengesindistributed |
deterministic model with using the average values of the quantumcomputing,”IEEENetwork,vol.34,no.1,pp.137–143,2020. |
[16] L. M. Haji, S. Zeebaree, O. M. Ahmed, A. B. Sallow, K. Jacksi, |
uncertain parameters. The cost of deploying the on-demand |
andR.R.Zeabri,“Dynamicresourceallocationfordistributedsystems |
quantum computer varies. The deployed quantum computer andcloudcomputing,”TESTEngineering&Management,vol.83,no. |
in the first stage is chosen at random in the random model. May/June2020,pp.22417–22426,2020. |
[17] S. Chaisiri, B.-S. Lee, and D. Niyato, “Optimization of resource |
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