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Figure 8 compares the total costs of the three models. The
provisioning cost in cloud computing,” IEEE transactions on services
proposed model, as we can see, delivers the lowest total cost. Computing,vol.5,no.2,pp.164–177,2011.
Additionally, the EVF and random models cannot adapt to [18] G. S. Ravi, K. N. Smith, P. Gokhale, and F. T. Chong, “Quantum
computing in the cloud: Analyzing job and machine characteristics,”
the variations in costs of the on-demand quantum computers,
in 2021 IEEE International Symposium on Workload Characterization
while the proposed scheme can always achieve the most cost- (IISWC). IEEE,2021,pp.39–50.
effective solution. [19] G.S.Ravi,K.N.Smith,P.Murali,andF.T.Chong,“Adaptivejoband
resource management for the growing quantum cloud,” in 2021 IEEE
VI. CONCLUSION International Conference on Quantum Computing and Engineering
(QCE). IEEE,2021,pp.301–312.
Inthispaper,wehaveproposedanoptimalresourcealloca- [20] C. Cicconetti, M. Conti, and A. Passarella, “Resource allocation in
tion scheme to efficiently utilize quantum resources in DQC quantum networks for distributed quantum computing,” in 2022 IEEE
International Conference on Smart Computing (SMARTCOMP), 2022,
to compute complex computational tasks at scale. We have
pp.124–132.
formulated a two-stage stochastic programming to minimize [21] R.Jozsa,“Fidelityformixedquantumstates,”Journalofmodernoptics,
the total deployment cost under uncertainties of the demands vol.41,no.12,pp.2315–2323,1994.
[22] “HowcanquantumcomputingbeusefulforMachineLearning,”https:
of computational tasks, the computing power of quantum
//www.kdnuggets.com/2019/04/quantum-computing-machine-learning.
computers, and the quantum characteristics over quantum html.
networks. The experimental findings demonstrate that the [23] “Qubits meet materials science,” pp. 869–869, Oct 2021. [Online].
Available:https://doi.org/10.1038/s41578-021-00378-w
proposed scheme can minimize the total deployment cost
[24] “IBMQuantumLabAPIErrorCode,”https://quantum-computing.ibm.
under uncertainty. Other methods, such as dynamic resource com/lab/docs/iql/manage/errors,accessed:2022-07-28.
allocation, and other factors, such as the deployment of [25] Y. Cao, Y. Zhao, Q. Wang, J. Zhang, S. X. Ng, and L. Hanzo, “The
evolution of quantum key distribution networks: On the road to the
quantumcomputersacrossalongdistanceandtheuncertainty
qinternet,” IEEE Communications Surveys & Tutorials, vol. 24, no. 2,
of the time required to accomplish computing tasks, can be pp.839–894,2022.
considered for future research. [26] J. R. Birge and F. Louveaux, Introduction to stochastic programming.
SpringerScience&BusinessMedia,2011.
REFERENCES [27] “GAMS,” https://www.gams.com/latest/docs/UG ModelSolve.html, ac-
cessed:2022-09-05.
[1] “IBMQuantum,”https://www.ibm.com/quantum,accessed:2022-07-30.
[2] “QuantumAI,”https://quantumai.google/hardware.
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Quantum Computational Complexity
John Watrous
InstituteforQuantumComputingandSchoolofComputerScience
UniversityofWaterloo,Waterloo,Ontario,Canada.
8002
Article outline
I. Definitionofthesubjectanditsimportance
rpA
II. Introduction
III. Thequantumcircuitmodel
12 IV. Polynomial-timequantumcomputations
V. Quantumproofs
]hp-tnauq[
VI. Quantuminteractiveproofsystems
VII. Otherselectednotionsinquantumcomplexity
VIII. Futuredirections
IX. References
Glossary
1v1043.4080:viXra
Quantumcircuit.
Aquantumcircuitisanacyclicnetworkofquantumgatesconnectedbywires: thegatesrepresent
quantumoperationsandthewiresrepresentthequbitsonwhichtheseoperationsareperformed.
Thequantumcircuit modelisthemostcommonlystudiedmodelofquantumcomputation.
Quantumcomplexityclass.
Aquantumcomplexityclassisacollectionofcomputationalproblemsthataresolvable byacho-
sen quantum computational model that obeys certain resource constraints. For example, BQP is
thequantumcomplexityclassofalldecisionproblemsthatcanbesolvedinpolynomialtimebya
quantumcomputer.
Quantumproof.
A quantum proof is a quantum state that plays the role of a witness or certificate to a quan-
tumcomputerthatrunsaverificationprocedure. ThequantumcomplexityclassQMAisdefined
by this notion: it includes all decision problems whose yes-instances are efficiently verifiable by
meansofquantumproofs.
Quantuminteractiveproofsystem.
Aquantuminteractiveproofsystemisaninteractionbetweenaverifierandoneormoreprovers,
involving theprocessingand exchangeofquantuminformation, wherebytheproversattemptto
convincetheverifieroftheanswertosomecomputationalproblem.
1
I Definition of the subject and its importance
The inherent difficulty, or hardness, of computational problems is a fundamental concept in com-
putationalcomplexitytheory. Hardnessistypicallyformalized intermsoftheresourcesrequired
by different models of computation to solve a given problem, such as the number of steps of a
deterministicTuringmachine. Avariety ofmodelsandresourcesare oftenconsidered,including
deterministic, nondeterministic and probabilistic models; time and space constraints; and inter-
actionsamongmodelsofdifferingabilities. Manyinterestingrelationshipsamongthesedifferent
modelsandresourceconstraintsareknown.
Onecommonfeatureofthemostcommonlystudiedcomputationalmodelsandresourcecon-
straintisthattheyarephysically motivated. Thisisquitenatural,giventhatcomputersarephysical
devices,andtoasignificantextentitistheirstudythatmotivatesanddirectsresearchoncompu-
tational complexity. The predominant example is the class of polynomial-time computable func-
tions,whichultimatelyderivesitsrelevancefromphysicalconsiderations;foritisamathematical
abstraction of the class of functions that can be efficiently computed without error by physical
computingdevices.
Inlightofitscloseconnectiontothephysicalworld,itseemsonlynaturalthatmodernphysical
theoriesshould be consideredin thecontextofcomputational complexity. In particular, quantum
mechanicsisaclear candidateforaphysicaltheorytohavethepotentialforimplications, ifnotto