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Quantum Computing Algorithms

Name: Quantum Computing Algorithms
Author: Barry Burd
ISBN: 9781804617373

by Barry Burd

September 2023

Intermediate to advanced

342 pages

8h 46m

English

Packt Publishing

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Quantum Computing Algorithms
ContributorsAbout the authorAbout the reviewers
Preface
Who this book is forWhat this book coversTo get the most out of this bookDownload the example code filesConventions usedGet in touchShare Your ThoughtsDownload a free PDF copy of this book
Introduction to Quantum Computing
What is quantum computing?Baby steps toward quantum computingProgramming a quantum computerThe future of quantum computingFurther reading
Part 1 Nuts and Bolts
Chapter 1: New Ways to Think about Bits
Technical requirementsBits and logic gatesBinary representationWorking with matricesVectorsMatrix multiplicationThe tensor productCombining gates and bitsMatrix representation of bits and gatesMatrix operations and computer logicJupyter notebooksCreating and displaying valuesWhich values are (or are not) defined?Stopping a run of the codeSaving your workCopying this book’s example codeMatrices in PythonSummaryQuestions
Chapter 2: What Is a Qubit?
Technical requirementsA qubit’s values between 0 and 1Are qubits useful?How to make a qubitWhat does “between |0⟩ and |1⟩” mean?Qubits and QiskitCreating and running a quantum circuitUnderstanding the Qiskit codeVariations of this chapter’s codeSummaryQuestions
Chapter 3: Math for Qubits and Quantum Gates
Matrices for qubit states and operationsQubits on the Bloch sphereMore points on the Bloch sphereThe X gateThe Hadamard rotationCombining gates along a single wireReversible operationsReversing a matrix operationUnitary matricesRotating the Bloch sphere around an axisExperimenting with rotationsWhat is a radian?A taste of trigonometrySummaryQuestions
Chapter 4: Qubit Conspiracy Theories
Multi-qubit gatesCNOT and flipped CNOT gatesSWAP gateToffoli gateMagic tricks with multi-qubit gatesIntroducing entanglementEntanglement with matricesWorking with QiskitThe four Bell statesRole of entanglement in quantum computingQubits don’t plan aheadWhat quantum theory predictsWhat would happen if there were hidden variables?Bell’s experiment in QiskitCombining probabilitiesAddition (either this event or that event)Subtraction (not this event)Multiplication (this event and that event)Division (this event assuming that event)SummaryQuestionsFurther readings
Part 2 Making Qubits Work for You
Chapter 5: A Fanciful Tale about Cryptography
Technical requirementsSharing secretsAdding Hadamard gatesIntroducing randomnessAdding more randomnessAlice and Bob compare some of their bitsSome remaining bits form the secret keyIs the BB84 algorithm useful?You can’t copy a qubitQiskit code for the BB84 algorithmCreating the circuitsRunning the quantum circuitsDisplaying the outcomeGetting more information about a circuitSummaryQuestions

Chapter 6: Quantum Networking and Teleportation
Technical requirementsTransmitting bits and qubitsClassical networksQuantum networksTeleporting a qubitQuantum operations for teleportationTeleportation versus cloningCoding the teleportation circuitryCreating registersAdding gates to the registersRunning the quantum circuitSummaryQuestionsFurther reading
Part 3 Quantum Computing Algorithms
Chapter 7: Deutsch’s Algorithm
Technical requirementsDescribing Deutsch’s problemAlgorithmsFunctionsConstant and balanced functionsDeutsch’s problemSolving Deutsch’s problemPhase kickbackDetecting a CNOT gateEmbedding a function in quantum circuitryCreating oraclesPutting it all togetherDeutsch’s algorithm F.A.Q.Coding Deutsch’s algorithmSummaryQuestions
Chapter 8: Grover’s Algorithm
How long does it take to find what you need?The idea behind Grover’s algorithmThe oracleThe diffuserSearching among eight itemsSearching among any number of itemsThe optimal number of Grover iterate applicationsMatrices for Grover’s algorithmA matrix for the oracleA matrix for the diffuserCoding Grover’s algorithm with matricesWhen to use Grover’s algorithmEncrypting passwordsFinding better approximationsSatisfying Boolean expressionsCoding Grover’s algorithm with high-level functionsGates and circuits for Grover’s algorithmGates for the oracleGates for the diffuserCoding Grover’s algorithm with quantum gatesEpilogue – what does have to do with Grover’s algorithm?SummaryQuestions
Chapter 9: Shor’s Algorithm
Technical requirementsA popular encryption schemeAn example of RSA encryptionHow Shor’s algorithm worksThe role of a period in factoring a numberRepeated squaringComplex numbersComplex number basicsUnitary matricesThe connection between complex numbers and circlesFinding a sequence’s periodThe QFT matrixShoring up your knowledgeIllustrating Shor’s algorithm with Qiskit codeTesting the QFTAnother implementation of Shor’s algorithmSummaryFurther readingQuestions
Part 4 Beyond Gate-Based Quantum Computing
Chapter 10: Some Other Directions for Quantum Computing
What is reducibility?Quantum simulationQuantum annealingQuantum neural netsSolving unsolvable problemsSummaryReferences
Assessments
Chapter 1, New Ways to Think about BitsChapter 2, What Is a Qubit?Chapter 3, Math for Qubits and Quantum GatesChapter 4, Qubit Conspiracy Theories Chapter 5, A Fanciful Tale about CryptographyChapter 6, Quantum Networking and TeleportationChapter 7, Deutsch’s AlgorithmChapter 8, Grover’s AlgorithmChapter 9, Shor’s Algorithm
Index
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Content preview from Quantum Computing Algorithms

Preface

Several years ago, in the waiting room of a physician’s office, I picked up a copy of the magazine Nature. One of the issue’s articles lit a fire under me and led me to the study of quantum computing. At first, I was perplexed. How can this model of computing be so different from the kind of computing we know and love? Why do these strange circuits yield correct answers to mathematical problems?

Being a teacher, I knew that the best way to learn something was to try explaining it to someone else. So I decided to offer a one-semester course for university students. A typical quantum computing introduction involves programming, physics, and abstract mathematics. I wanted my course to attract students from many disciplines, and frankly, ...

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Quantum Computing Algorithms

by Barry Burd

Preface

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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