book

Quantum Computing

by Andrew Glasner

September 2025

Intermediate to advanced

424 pages

12h 9m

English

No Starch Press

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What Is Quantum Computing?Why Should You Read This Book?Who This Book Is ForWhat You’ll LearnHow We’ll Do ItUsing MetaphorsUsing MathReading MathProving ThingsIs Quantum Weird?What You’ll NeedWho Wrote This Book?OverviewPart I: States, Operators, and SystemsPart II: Quantum Algorithms

Electronic Playing CardsStatesSuperpositionInitializationMeasurementOperating on CardsAmplitudes and ProbabilitiesInterferenceEntanglementEntangled CardsEntanglement in ActionSummary
Getting StartedPostulate 1NumbersSets and ListsTypes of NumbersComplex NumbersWorking with iVisualizationConjugationWorking with Complex NumbersList StructureVectorsLinearityBasesThe Dot ProductUsing the Dot ProductProjectionChange of BasisThe Inner ProductDefining the Inner ProductFinding a Complex Vector’s MagnitudeChoosing Which Term to ConjugateProjection with the Inner ProductBraket NotationLooking at the BraketConjugating the BraketQubitsSummary
Postulate 2Linear OperatorsOperators I, X, and HThe Identity Operator IThe NOT Operator XThe Hadamard Operator HA Few Matrix OperationsUnitary OperatorsNaming a Matrix ElementRevisiting I, X, and HPutting It All TogetherSummary
Hello, World!Introducing Hello, XWorld!SuperpositionsProperties of HQugates and Basis StatesInitializing with HInterferenceSummary
Postulate 3Combining Quantum StatesThe Tensor ProductProduct StatesExploring Product StatesMore QubitsQuantum Algorithm DiagramsSystems of QugatesHorizontal Systems of QugatesVertical Systems of QugatesHorizontal and Vertical RulesA Circuit AnalysisAnalysis by AlgebraAnalysis by Matrix ElementsAnalysis by DirectionThe No-Cloning TheoremThe CX QugateCX as a SwitchCX as a CopierEntanglementEntangled PairsOther Controlled QugatesOther Multi-Qubit QugatesSingle-Qubit QugatesSummary
The Main Ideas of MeasurementMeasuring QubitsPostulate 4MetersExperimentsMeasuring Hello, World!Measuring X |0⟩Measuring H |0⟩Measuring HH |0⟩Measuring an Unequal SuperpositionAmplitudes from ProjectionThe Outer ProductBack to MeasurementMeasuring Multiple QubitsMeasuring Some QubitsComputing ProbabilitiesReturning to MeasurementPartial MeasurementMeasurement and EntanglementIntroducing Bell StatesMeasuring Bell StatesPhaseGlobal PhaseRelative Phase and InterferenceSummary
The Teleportation Thought ExperimentThe Teleportation State |τ ⟩The Teleportation ProcessBuilding |τ ⟩Alice Measures Her QubitsAlice Tells Bob the MeasurementsBob Recovers |σ⟩Drawing the Teleportation ProtocolProbabilistic TeleportationSummary
Deutsch’s ProblemOraclesQuantum OraclesPromise OraclesQuantum ParallelismThe Three Steps of Deutsch’s AlgorithmStep 1: InitializationStep 2: Querying the OracleStep 3: Postprocessing and MeasurementPhase KickbackAnalyzing Deutsch’s Algorithm with Phase KickbackDeutsch’s Algorithm RevisitedCX TerminologyReturn to Quantum ParallelismRevisiting Phase KickbackSummary
Introducing Deutsch–JozsaThe Three Steps of Deutsch–Jozsa’s AlgorithmStep 1: InitializationStep 2: Querying the OracleStep 3: Postprocessing and MeasurementResults in Constant and Balanced CasesA Constant FunctionA Balanced FunctionActual Results of Deutsch–Jozsa’s AlgorithmWhy Does the Math Work So Well?Summary
The Classical SolutionThe Bernstein–Vazirani CircuitCircuit Analysis After Deutsch–JozsaRunning the AlgorithmSimplifying with a Quantum IdentitySummary
Exponential GrowthSimon’s OracleThe Classical SolutionThe Quantum Part of the AlgorithmRewriting x and MeasuringCombining the Quantum OutputsAn Example of Simon’s AlgorithmThe Balancing ActSummary
An Overview of Grover’s AlgorithmReflectionsThe Stages of Grover’s OracleG1: MarkingG2: DiffusionIterating the Grover OracleAn Example of Grover’s AlgorithmObservations and DiscussionSummary
Primes and EncryptionShor’s AlgorithmPeriod FindingAnalyzing the CircuitApplying the QFTFinding the Probability of |k⟩Connecting to Prime FactoringAn Example of Shor’s AlgorithmDiscussionSummary
Further IdeasSuperdense CodingPOVM and the Density MatrixQuantum EncryptionQuantum Error CorrectionOther DiagramsQuantum AdvantageFurther ReadingQuantum Mechanics BooksQuantum Computing BooksQuantum Computing Lecture NotesQuantum Computing OnlineQuantum Computing ResourcesSimulatorsOther SoftwareReal HardwareDrawing CircuitsGetting HelpThe Philosophy of Quantum MechanicsApplicationsMaze SolvingRay TracingGamesOther ApplicationsWrapping Up

Overview

What if you had a computer that could process billions of different inputs at the same time?

Quantum computing is a radically new way to think about algorithms and data. It can feel mysterious or technically challenging, but it doesn’t have to be. If you want to understand how quantum computers work—and how to program them—this friendly, self-contained guide is for you.

This approachable yet rigorous book walks you step-by-step through quantum computing fundamentals, such as superposition, quantum gates, interference, entanglement, and measurement, then teaches you how to write real quantum programs.

Along the way, you’ll:

Understand how to store and transform quantum information
Grasp the surprising process of quantum measurement
Explore Simon’s, Grover’s, and Shor’s algorithms
Write and run your own quantum code using free simulators and live hardware

Author Andrew Glassner is known for turning complex topics into accessible and enjoyable learning experiences. In this book, he brings visual thinking, clarity, context, and precision to the strange and fascinating world of quantum programming. All the ideas and math are built up slowly so you’ll master every step.

Whether you’re a programmer, student, educator, scientist, poet, or anyone else who loves new ideas that stretch your mind, this is the guide that will take you from “What is a qubit?” to writing and running working quantum algorithms with curiosity, creativity, and confidence.