book

Quantum Computing Explained

by David McMahon

December 2007

Intermediate to advanced

332 pages

7h 28m

English

Wiley-IEEE Press

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Classical InformationInformation Content in a SignalEntropy and Shannon’S Information TheoryProbability BasicsEXERCISES
The QubitVector SpacesLinear Combinations of VectorsUniqueness of a Spanning SetBasis and DimensionInner ProductsOrthonormalityGram-Schmidt OrthogonalizationBra-Ket FormalismThe Cauchy-Schwartz And Triangle InequalitiesSummaryExercises
ObservablesThe Pauli OperatorsOuter ProductsThe Closure RelationRepresentations of Operators Using MatricesOuter Products and Matrix RepresentationsMatrix Representation of Operators in Two-Dimensional SpacesDefinition: The Pauli MatricesHermitian, Unitary, And Normal OperatorsEigenvalues and EigenvectorsSpectral DecompositionThe Trace Of An OperatorImportant Properties of the TraceThe Expectation Value of an OperatorProjection OperatorsPOSITIVE OPERATORSCommutator AlgebraThe Heisenberg Uncertainty PrinciplePolar Decomposition and Singular ValuesThe Postulates of Quantum MechanicsExercises
Representing Composite States in Quantum MechanicsComputing Inner ProductsTensor Products of Column VectorsOperators and Tensor ProductsTensor Products of MatricesExercises

The Density Operator For a Pure StateThe Density Operator For a Mixed StateKey Properties of a Density OperatorCharacterizing Mixed StatesThe Partial Trace And The Reduced Density OperatorThe Density Operator and the Bloch VectorEXERCISES
Distinguishing Quantum States and MeasurementProjective MeasurementsMeasurements on Composite SystemsGeneralized MeasurementsPositive Operator-Valued MeasuresExercises
Bell’S TheoremBipartite Systems and the Bell BasisWhen is a State Entangled?The Pauli RepresentationEntanglement FidelityUsing Bell States For Density Operator RepresentationSchmidt DecompositionPurificationExercises
Classical Logic GatesSingle-Qubit GatesMore Single-Qubit GatesExponentiationThe Z–Y DecompositionBasic Quantum Circuit DiagramsControlled GatesGate DecompositionExercises
Hadamard GatesThe Phase GateMatrix Representation of Serial and Parallel OperationsQuantum InterferenceQuantum Parallelism and Function EvaluationDeutsch-Jozsa AlgorithmQuantum Fourier TransformPhase EstimationShor’S AlgorithmQuantum Searching And Grover’S AlgorithmExercises
TeleportationThe Peres Partial Transposition ConditionEntanglement SwappingSuperdense CodingExercises
A Brief Overview of Rsa EncryptionBasic Quantum CryptographyAn Example Attack: The Controlled Not AttackThe B92 ProtocolThe E91 Protocol (Ekert)Exercises
Single-Qubit ErrorsQuantum Operations And Krauss OperatorsThe Depolarization ChannelThe Bit Flip and Phase Flip ChannelsAmplitude DampingPhase DampingQuantum Error CorrectionExercises
The No-Cloning TheoremTrace DistanceFidelityEntanglement of Formation and ConcurrenceInformation Content and EntropyExercises
Adiabatic ProcessesAdiabatic Quantum ComputingExercises
Cluster StatesAdjacency MatricesStabilizer StatesAside: Entanglement WitnessCluster State ProcessingExercises

Overview

A self-contained treatment of the fundamentals of quantum computing

This clear, practical book takes quantum computing out of the realm of theoretical physics and teaches the fundamentals of the field to students and professionals who have not had training in quantum computing or quantum information theory, including computer scientists, programmers, electrical engineers, mathematicians, physics students, and chemists. The author cuts through the conventions of typical jargon-laden physics books and instead presents the material through his unique "how-to" approach and friendly, conversational style.

Readers will learn how to carry out calculations with explicit details and will gain a fundamental grasp of:

*Quantum mechanics

*Quantum computation

*Teleportation

*Quantum cryptography

*Entanglement

*Quantum algorithms

*Error correction

A number of worked examples are included so readers can see how quantum computing is done with their own eyes, while answers to similar end-of-chapter problems are provided for readers to check their own work as they learn to master the information.

Ideal for professionals and graduate-level students alike, Quantum Computing Explained delivers the fundamentals of quantum computing readers need to be able to understand current research papers and go on to study more advanced quantum texts.