Table Of ContentHybrid Quantum
Metaheuristics
Series Page
Quantum Machine Intelligence Series
SERIES EDITORS
Siddhartha Bhattacharyya, Rajnagar Mahavidyalaya, Birbhum, India
Elizabeth C. Behrman, Wichita State University, USA
Hybrid Quantum Metaheuristics
Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan
Cruz-Aceves
Quantum Machine Intelligence
Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan
Cruz-Aceves
For more information about this series, please visit: https://www.rout-
ledge.com/Quantum-Machine-Intelligence/book-series/QMI
Hybrid Quantum
Metaheuristics
Theory and Applications
Edited by
Siddhartha Bhattacharyya
Mario Köppen
Elizabeth Behrman
Ivan Cruz-Aceves
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks
does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of
MATLAB® software or related products does not constitute endorsement or sponsorship by The
MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.
First edition published [2022]
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CRC Press is an imprint of Taylor & Francis Group, LLC
© 2022 selection and editorial matter, Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman,
Ivan Cruz-Aceves, individual chapters, the contributors
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ISBN: 9780367751562 (hbk)
ISBN: 9781032254616 (pbk)
ISBN: 9781003283294 (ebk)
DOI: 10.1201/9781003283294
Typeset in Nimbus font CMR10
by KnowledgeWorks Global Ltd.
Dedication
SiddharthawouldliketodedicatethisvolumetolateProf.John
StewartBell,FRS,theoriginatorofBell’stheorem,animportant
theoreminquantumphysicsregardinghiddenvariabletheories.
ElizabethwouldliketodedicatethisvolumetoJPK,EJB,andJFB;
andtothememoryofCFB.
MariowouldliketodedicatethisbooktotheSchro¨dinger’scat.
Ivanwouldliketodedicatethisvolumetohislovelyfamily,hiswife
Mary,hischildrenIvanandYusef,andhismotherBety.
Contents
Editors.....................................................................................................................xiii
Preface.....................................................................................................................xix
Contributors..........................................................................................................xxiii
Chapter1 AnIntroductoryIllustrationtoQuantum-InspiredMetaheuristics..1
1.1 Introduction.............................................................................1
1.2 Quantum-InspiredMetaheuristics..........................................2
1.2.1 LocalSearchMetaheuristics......................................3
1.2.2 ConstructiveMetaheuristics.......................................4
1.2.3 Population-basedMetaheuristics...............................6
1.2.4 HybridMetaheuristics................................................7
1.3 Entanglement-InducedOptimization......................................7
1.4 W-stateEncodingofOptimizationAlgorithms......................8
1.5 QuantumSystem-basedOptimization....................................9
1.5.1 Bi-levelQuantumSystem-basedOptimization..........9
1.5.2 Multi-levelQuantumSystem-basedOptimization..10
1.6 ApplicationsofQuantum-InspiredMetaheuristics...............11
1.7 Conclusion............................................................................14
Chapter2 A Quantum-Inspired Approach to Collective Combine Basic
Classifiers......................................................................................21
2.1 Introduction...........................................................................21
2.2 BaggingMethod...................................................................21
2.3 ClassifiersBasedonSimilarityofObjects...........................22
2.4 StatisticalClassificationAlgorithms.....................................24
2.5 ClassifiersBasedonClassSeparabilityinAttributeSpace..25
2.6 LogicalClassificationAlgorithms .......................................26
2.7 NeuralNetworks...................................................................27
2.8 MethodsofCombiningBasicClassifiers.............................27
2.8.1 Voting.......................................................................27
2.8.2 Stacking....................................................................28
2.8.3 EnsembleSelection..................................................28
2.8.3.1 The<<naive>>BayesianClassifier.....30
2.8.4 Quantum-InspiredMetaheuristicsMethod..............30
2.9 Conclusion............................................................................32
vii
viii Contents
Chapter3 FunctionOptimizationUsingIBMQ............................................37
3.1 Introduction...........................................................................37
3.2 FunctionOptimization..........................................................38
3.2.1 DifficultiesinOptimizationMethods......................38
3.2.2 DefinitionofMulti-objectiveOptimization
Problem(MOOP).....................................................38
3.2.3 DifferencesbetweenSOOPsandMOOPs...............40
3.3 ModernOptimizationProblem-SolvingTechniques............40
3.3.1 GeneticAlgorithm...................................................40
3.3.2 SimulatedAnnealing................................................41
3.3.3 ParticleSwarmOptimization...................................41
3.3.4 BatAlgorithm..........................................................42
3.3.5 CuckooSearchAlgorithm........................................42
3.3.6 FuzzySystem...........................................................42
3.3.7 NeuralNetwork-BasedOptimization......................43
3.4 QuantumComputingandOptimizationAlgorithms............43
3.4.1 QuantumComputing................................................43
3.4.2 OptimizationUsingQuantumComputing...............44
3.5 FeaturesofIBMQExperience.............................................45
3.6 CircuitComposerIBMQ.....................................................45
3.7 QISKitinIBMQ..................................................................47
3.7.1 Creating 5-qubit Circuit with the Help of
QISKitinIBMQ.....................................................47
3.7.2 TestingtheCircuitUsingIBMQuantum
Computer..................................................................48
3.8 OptimizationUsingIBMQ..................................................51
3.9 Conclusion............................................................................53
Chapter4 MultipartiteAdaptiveQuantum-InspiredEvolutionaryAlgorithm
toReducePowerLosses................................................................57
4.1 Introduction...........................................................................57
4.2 LiteratureReview..................................................................60
4.3 ProblemFormulation............................................................64
4.4 PowerFlow...........................................................................66
4.5 Algorithm..............................................................................70
4.6 ResultsandDiscussion.........................................................75
4.7 Conclusions...........................................................................88
4.8 ParametersofIEEEBenchmarkTestBusSystem................92
Chapter5 Quantum-InspiredMantaRayForagingOptimizationAlgorithm
forAutomaticClusteringofColorImages....................................95
5.1 Introduction...........................................................................95
5.2 LiteratureReview..................................................................96
Contents ix
5.3 FundamentalsofQuantumComputing.................................97
5.3.1 RotationGate...........................................................98
5.3.2 Pauli-XGate.............................................................98
5.4 ValidityMeasurementofClustering.....................................98
5.5 OverviewofMantaRayForagingOptimization
Algorithm..............................................................................99
5.6 ProposedMethodology.......................................................100
5.7 ExperimentalResultsandAnalysis....................................102
5.7.1 DevelopmentalEntertainment................................103
5.7.2 DatasetUsed..........................................................103
5.7.3 ClusteredImages....................................................103
5.7.4 SensitivityAnalysisofQIMRFO...........................103
5.7.5 AnalysisofExperimentalResults..........................107
5.8 ConclusionandFutureScope.............................................108
Chapter6 Automatic Feature Selection for Coronary Stenosis Detection in
X-RayAngiograms......................................................................117
6.1 Introduction.........................................................................117
6.2 Background.........................................................................120
6.2.1 FeatureExtraction..................................................120
6.2.1.1 PixelIntensity-basedFeatures...............120
6.2.1.2 TextureFeatures....................................121
6.2.1.3 MorphologicFeatures............................122
6.2.2 FeatureSelection....................................................124
6.2.3 SupportVectorMachines.......................................125
6.2.4 QuantumGeneticAlgorithm..................................126
6.3 ProposedMethod................................................................130
6.4 ExperimentDetails.............................................................133
6.5 Results.................................................................................134
6.6 Conclusion..........................................................................136
Chapter7 QuantumPreprocessingforDCNNinAtherosclerosis
Detection......................................................................................141
7.1 Introduction.........................................................................141
7.2 RelatedWork......................................................................142
7.3 MathematicalFoundations..................................................145
7.3.1 QuantumComputing..............................................145
7.3.1.1 QubitStates...........................................146
7.3.1.2 QubitOperations...................................147
7.3.1.3 QubitMeasurements..............................149
7.3.2 ConvolutionalNeuralNetworks............................149
7.3.2.1 ConvolutionalLayer..............................150
7.3.2.2 PoolingLayer........................................150
7.3.2.3 FullyConnectedLayer..........................151
