Hands-On Quantum Machine Learning With Python Volume 1: Get Started

435 Pages·2021·5.201 MB·English

by  Dr. Frank Zickert

Hands-On Quantum Machine
Learning With Python
Volume 1: Get Started
Dr. Frank Zickert
PyQML
Copyright©2021Dr. FrankZickert
PUBLISHEDBYPYQML
www.pyqml.com
Thecontentsofthisbook, unlessotherwiseindicated, areCopyright©2021
Dr. FrankZickert,pyqml.com. Allrightsreserved. Bookslikethisaremade
possible by the time invested by the authors. If you received this book and
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Release1.0,May2021
Contents
1 Introduction ............................................... 7
1.1 WhoThisBookIsFor ........................................... 7
1.2 BookOrganization .............................................. 9
1.3 WhyShouldIBotherWithQuantumMachineLearning? ......... 10
1.4 QuantumMachineLearning‐BeyondTheHype ................. 11
1.4.1 WhatisMachineLearning? ....................................... 11
1.4.2 WhatisQuantumComputing? .................................... 13
1.4.3 HowDoesMachineLearningWork? ................................ 15
1.4.4 WhatTasksAreQuantumComputersGoodAt? ...................... 16
1.4.5 TheCaseForQuantumMachineLearning .......................... 18
1.5 QuantumMachineLearningInTheNISQEra .................... 19
1.6 IlearnedQuantumMachineLearningTheHardWay ............. 21
1.7 QuantumMachineLearningIsTaughtTheWrongWay .......... 24
1.8 ConfiguringYourQuantumMachineLearningWorkstation ...... 26
1.8.1 Python ........................................................ 27
1.8.2 Jupyter ........................................................ 27
1.8.3 LibrariesandPackages .......................................... 27
1.8.4 VirtualEnvironment ............................................ 28
1.8.5 ConfiguringUbuntuForQuantumMachineLearningwithPython ...... 28
1.8.6 HowToSetupJupyterLabForQuantumComputing‐‐‐OnWindows ..... 30
2 Binary Classification .................................... 33
2.1 PredictingSurvivalOnTheTitanic ............................ 33
2.2 GettheDataset ............................................... 34
2.3 Lookatthedata .............................................. 35
2.4 DataPreparationandCleaning ................................ 38
2.4.1 MissingValues .................................................. 38
2.4.2 Identifiers ...................................................... 40
2.4.3 HandlingTextandCategoricalAttributes ........................... 42
2.4.4 FeatureScaling ................................................. 43
2.4.5 TrainingandTesting ............................................ 45
2.5 Baseline ..................................................... 46
2.6 ClassifierEvaluationandMeasures ............................ 49
2.7 UnmasktheHypocriteClassifier ............................... 53
3 Qubit and Quantum States ............................. 62
3.1 ExploringtheQuantumStates ................................. 62
3.2 VisualExplorationOfTheQubitState .......................... 72
3.3 BypassingTheNormalization .................................. 74
3.4 ExploringTheObserverEffect ................................. 79
3.5 ParameterizedQuantumCircuit ............................... 84
3.6 VariationalHybridQuantum‐ClassicalAlgorithm ............... 89
4 Probabilistic Binary Classifier ........................ 100
4.1 TowardsNaïveBayes ......................................... 101
4.2 Bayes'Theorem ............................................. 105
4.3 GaussianNaïveBayes ........................................ 109
5 Working with Qubits ................................... 113
5.1 YouDon'tNeedToBeAMathematician ....................... 113
5.2 QuantumicMath‐AreYouReadyForTheRedPill? ............ 124
5.3 IfYouWantToGambleWithQuantumComputing… ............ 134
6 Working With Multiple Qubits ......................... 147
6.1 Hands‐OnIntroductionToQuantumEntanglement ............ 147
6.2 TheEquationEinsteinCouldNotBelieve ...................... 159
6.2.1 SingleQubitSuperposition ...................................... 160
6.2.2 QuantumTransformationMatrices ............................... 161
6.2.3 TransformingSingleQubits ...................................... 162
6.2.4 Two‐QubitStates ............................................... 162
6.2.5 Two‐QubitTransformations ..................................... 164
6.2.6 Entanglement ................................................. 167
6.3 QuantumProgrammingForNon‐mathematicians .............. 173
6.3.1 Representingamarginalprobability .............................. 176
6.3.2 Calculatethejointprobability .................................... 178
6.3.3 Calculatetheconditionalprobability .............................. 186
7 Quantum Naïve Bayes ................................. 204
7.1 Pre‐processing .............................................. 206
7.2 PQC ......................................................... 209
7.3 Post‐Processing ............................................. 222
8 Quantum Computing Is Different ..................... 225
8.1 TheNo‐CloningTheorem ..................................... 225
8.2 HowToSolveAProblemWithQuantumComputing ............ 231
8.3 TheQuantumOracleDemystified ............................. 244
9 Quantum Bayesian Networks ......................... 253
9.1 BayesianNetworks .......................................... 255
9.2 ComposingQuantumComputingControls ..................... 259
9.3 Circuitimplementation ...................................... 274
10 Bayesian Inference .................................... 281
10.1 LearningHiddenVariables ................................... 282
10.2 EstimatingASingleDataPoint ............................... 283
10.3 EstimatingAVariable ....................................... 294
10.4 PredictSurvival ............................................. 316
11 The World Is Not A Disk ............................... 320
11.1 TheQubitPhase ............................................. 320
6
11.2 VisualizeTheInvisibleQubitPhase ........................... 333
11.2.1 TheZ‐gate .................................................... 334
11.2.2 Multi‐QubitPhase .............................................. 343
11.2.3 ControlledZ‐gate ............................................... 349
11.3 PhaseKickback ............................................. 351
11.4 QuantumAmplitudesandProbabilities ....................... 364
12 Working With The Qubit Phase ........................ 371
12.1 TheIntuitionOfGrover'sAlgorithm .......................... 372
12.2 BasicAmplitudeAmplification ............................... 377
12.3 Two‐QubitAmplification ..................................... 385
13 Search For The Relatives .............................. 397
13.1 TurningtheProblemintoaCircuit ............................ 400
13.2 MultipleResults ............................................. 416
14 Sampling ................................................ 420
14.1 ForwardSampling ........................................... 420
14.2 BayesianRejectionSampling ................................. 422
14.3 QuantumRejectionSampling ................................. 427
15 What's Next? ........................................... 434
1. Introduction
WelcometoHands-OnQuantumMachineLearningWithPython.Thisbook
isyourcomprehensiveguidetogetstartedwith“QuantumMachineLearning”
– the use of quantumcomputing for the computation of machinelearning
algorithms.
Hands-On Quantum Machine Learning With Python strives to be the per-
fect balance between theory taught in a textbook and the actual hands-on
knowledgeyou’llneedtoimplementreal-worldsolutions.
Inside this book, you will learn the basics of quantum computing and ma-
chinelearninginapracticalandappliedmanner. Andyouwilllearntouse
state-of-the-artquantummachinelearningalgorithms.
By the time you finish this book, you’ll be well equipped to apply quantum
machinelearningtoyourprojects. Then,youwillbeinthepolepositionto
becomea“QuantumMachineLearningEngineer”–thejobtobecomethesexi-
estjobofthe2020s.
1.1 Who This Book Is For
Thisbookisfordevelopers,programmers,students,andresearcherswho
haveatleastsome programmingexperienceand wanttobecomeproficient
inquantummachinelearning.
Don’tworryifyou’rejustgettingstartedwithquantumcomputingandma-
chine learning. We will begin with the basics, and we don’t assume prior
8 Chapter1.Introduction
knowledgeofmachinelearningorquantumcomputing. Soyouwillnotget
leftbehind.
If you have experience in machine learning or quantum computing, the re-
spective parts may repeat concepts you’re already familiar with. However,
this may make learning the corresponding new topic easier and provide a
slightlydifferentangletotheknown.
This book offers a practical, hands-on exploration of quantum machine
learning. Ratherthanworkingthroughtonsoftheory,wewillbuildupprac-
ticalintuitionaboutthecoreconcepts. Wewillacquiretheexactknowledge
weneedtosolvepracticalexampleswithlotsofcode. Stepbystep, youwill
extendyourknowledgeandlearnhowtosolvenewproblems.
Of course, we will do some math. Of course, we will cover a little physics.
But I don’t expect you to hold a degree in any of these two fields. We will
go through all the concepts we need. While this includes some mathemati-
calnotationandformulae,wekeepitattheminimumrequiredtosolveour
practicalproblems.
The theoretical foundation of quantum machine learning may appear over-
whelmingatfirstsight. But,beassuredthatitisnotharderthanlearninga
newprogramminglanguagewhenputintothepropercontextandexplained
conceptually. Andthisiswhat’sinsideHands-OnQuantumMachineLearn-
ingWithPython.
Of course, we will write code. A lot of code. Do you know a little Python?
Great! If you don’t know Python but another language, such as Java,
Javascript, or PHP, you’ll be fine, too. If you know programming concepts
(suchasif-thenelse-constructsandloops),thenlearningthesyntaxisapiece
ofcake. Ifyou’refamiliarwithfunctionalprogrammingconstructs,suchas
map,filter,andreduce,you’realreadywellequipped. Ifnot,don’tworry. We
willgetyoustartedwiththeseconstructs,too. Wedon’texpectyoutobease-
niorsoftwaredeveloper. Wewillgothroughallthesourcecode—linebyline.
By the time you finish the first few chapters of this book, you will be profi-
cientwithdoingthemath,understandingthephysics,andwritingthecode
youneedtograduatetothemoreadvancedcontent.
Thisbookisnotjustforbeginners. Thereisalotofadvancedcontentinhere,
too. Manychaptersof Hands-OnQuantumMachineLearningWithPython
cover, explain, andapplyquantummachinelearningalgorithmsdeveloped
inthelasttwoyears. Youcandirectlyapplytheinsightsthisbookprovides
in your job and research. The time you save by reading through Hands-On
QuantumMachineLearningWithPythonwillmorethanpayforitself.
1.2 BookOrganization 9
1.2 Book Organization
Machinelearningandquantumcomputingrelyonmath,statistics,physics,
andcomputerscience. Thisisalotoftheory. Coveringitallupfrontwould
beprettyexhaustiveandfillatleastonebookwithoutanypracticalinsight.
However, without understanding the underlying theoretical concepts, the
code examples on their own do not provide many practical insights, either.
Whilelibrariesfreeyoufromtediousimplementationdetails,thecode,even
thoughshort,doesnotexplainthecoreconcepts.
Thisbookprovidesthetheoryneededtounderstandthecodewe’rewriting
tosolveaproblem. Foronething, wecoverthetheorywhenitapplies, and
weneedittounderstandthebackgroundofwhatwearedoing. Secondly,we
willembedthetheoryintosolvingapracticalproblemanddirectlyseeitin
action.
As a result, the theory spreads among all the chapters, from simple to com-
plex. You may skip individual examples if you like. But you should have a
lookatthetheoreticalconceptsdiscussedineachchapter.
We start with a Variational Hybrid Quantum-Classical Algorithm to solve a
binary classification task. First, we have a detailed look at binary classifica-
tion in chapter 2. Then, in chapter 3, we introduce the basic concept of the
quantumbit,thequantumstate,andhowmeasurementaffectsit. Basedon
theseconcepts,webuildourfirstParameterizedQuantumCircuitanduseit
tosolveourbinaryclassificationtask. Suchahybridalgorithmcombinesthe
quantumstatepreparationandmeasurementwithclassicaloptimization.
Then, we learn how to work with single qubits (chapter 5) and with multi-
plequbits(chapter6). Andweexploretheastonishingphenomenonofquan-
tum entanglement. This serves as our basis to develop a Quantum Naïve
Bayesclassifier(chapter7). Inchapter8,wedivedeepintothespecificitiesof
howquantumcomputingisdifferentfromclassicalcomputingandhowwe
solveproblemsthequantumway. Itenablesustocreateandtrainaquantum
Bayesiannetwork(chapter9).
By now, you’ll be experienced in dealing with the probabilistic nature of
qubits. It’s time to take it one step further. We learn about the qubit phase
(chapter 11) and how we can use it to tap the potential of quantum systems
(chapter12). WeuseittosearchtherelativesofapassengeronboardtheTi-
tanic(chapter13)andapproximateavariable’sdistributioninourquantum
Bayesiannetwork. (chapter14).
YoucanfindthecompletesourcecodeofthisbookthisGithubrepository.
10 Chapter1.Introduction
1.3 Why Should I Bother With Quantum
Machine Learning?
In the recent past, we have witnessed how algorithms learned to drive cars
and beat world champions in chess and Go. Machine learning is being ap-
pliedtovirtuallyeveryimaginablesector, frommilitarytoaerospace, from
agriculturetomanufacturing,andfromfinancetohealthcare.
Butthesealgorithmsbecomeincreasinglyhardtotrainbecausetheyconsist
of billions of parameters. Quantum computers promise to solve such prob-
lemsintractablewithcurrentcomputingtechnologies. Moreover,theirabil-
ity to compute multiple states simultaneously enables them to perform an
indefinite number of superposed tasks in parallel. An ability that promises
toimproveandtoexpeditemachinelearningtechniques.
Unlike classical computers based on sequential information processing,
quantumcomputingusesthepropertiesofquantumphysics: superposition,
entanglement, and interference. But rather than increasing the available
computingcapacity,itreducesthecapacityneededtosolveaproblem.
Butquantumcomputingrequiresustochangethewaywethinkaboutcom-
puters. It requires a whole new set of algorithms. Algorithms that encode
andusequantuminformation. Thisincludesmachinelearningalgorithms.
Anditrequiresanewsetofdevelopers. Developerswhounderstandmachine
learning and quantum computing. Developers capable of solving practical
problems that have not been solved before. A rare type of developer. The
ability to solve quantum machine learning problems already sets you apart
fromalltheothers.
Quantummachinelearningpromisestobedisruptive. Althoughthismerger
ofmachinelearningandquantumcomputing,bothareasofactiveresearch,
islargelyintheconceptualdomain,therearealreadysomeexampleswhereit
isbeingappliedtosolvereal-lifeproblems. Google,Amazon,IBM,Microsoft,
andawholefleetofhigh-techstartupsstrivetobethefirsttobuildandsell
quantummachinelearningsystems.
The opportunity to study a technology right when it is about to prove its
supremacyisauniqueopportunity. Don’tmissit.