Quantum Computing: From Linear Algebra to Physical Realizations Book

From linear algebra to quantum computing
Basics of Vectors and Matrices
Vector Spaces Linear Dependence and Independence of Vectors Dual Vector Spaces Basis, Projection Operator, and Completeness Relation Linear Operators and Matrices Eigenvalue Problems Pauli Matrices Spectral Decomposition Singular Value Decomposition (SVD)
Tensor Product (Kronecker Product)
Framework of Quantum Mechanics
Fundamental Postulates Some Examples Multipartite System, Tensor Product, and Entangled State Mixed States and Density Matrices
Qubits and Quantum Key Distribution
Qubits Quantum Key Distribution (BB84 Protocol)
Quantum Gates, Quantum Circuit, and Quantum Computer
Introduction Quantum Gates Correspondence with Classical Logic Gates No-Cloning Theorem Dense Coding and Quantum Teleportation Universal Quantum Gates Quantum Parallelism and Entanglement
Simple Quantum Algorithms
Deutsch Algorithm Deutsch–Jozsa Algorithm and Bernstein–Vazirani Algorithm Simon’s Algorithm
Quantum Integral Transforms
Quantum Integral Transforms Quantum Fourier Transform (QFT)
Application of QFT: Period-Finding Implementation of QFT Walsh–Hadamard Transform Selective Phase Rotation Transform
Grover’s Search Algorithm
Searching for a Single File Searching for d Files
Shor’s Factorization Algorithm
The RSA Cryptosystem Factorization Algorithm Quantum Part of Shor’s Algorithm Probability Distribution Continued Fractions and Order-Finding Modular Exponential Function
Decoherence
Open Quantum System Measurements as Quantum Operations Examples Lindblad Equation
Quantum Error-Correcting Codes (QECC)
Introduction
3-Qubit Bit-Flip Code and Phase-Flip Code Shor’s 9-Qubit Code Calderbank–Shor–Steane (CSS) 7-Qubit QECC DiVincenzo–Shor 5-Qubit QECC
Physical realizations of quantum computing
DiVincenzo Criteria
Introduction DiVincenzo Criteria Physical Realizations Beyond DiVincenzo Criteria
NMR Quantum Computer
Introduction NMR Spectrometer Hamiltonian Implementation of Gates and Algorithms Time-Optimal Control of NMR Quantum Computer Measurements Preparation of Pseudopure State DiVincenzo Criteria
Trapped Ions
Introduction Electronic States of Ion as Qubit Ions in Paul Trap Ion Qubit Quantum Gates Readout DiVincenzo Criteria
Quantum Computing with Neutral Atoms
Introduction Trapping Neutral Atoms
1-Qubit Gate Quantum State Engineering of Neutral Atoms Preparation of Entangled Neutral Atoms DiVincenzo Criteria
Josephson Junction Qubits
Introduction Nanoscale Josephson Junctions and SQUIDs Charge Qubit Flux Qubit Quantronium Current-Biased Qubit Readout Coupled Qubits DiVincenzo Criteria
Quantum Computing with Quantum Dots
Introduction Mesoscopic Semiconductors Electron Charge Qubit Electron Spin Qubit DiVincenzo Criteria
Appendix: Solutions to Selected Exercises
Index