Quantum Computation and Quantum Information Simulation using Python: A gentle introduction

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PRELIMS.pdf Preface Author biography Shinil Cho Acknowledgments CH001.pdf Chapter 1 Two-level quantum systems 1.1 Vectors and matrices 1.1.1 Calculation rules of vectors and matrices 1.1.2 Combining two different vector spaces—direct product 1.2 Foundation of quantum mechanics 1.2.1 General properties of quantum states 1.3 Quantum state vectors 1.3.1 Two-level quantum state vector: qbit 1.3.2 Projection operators for spin states 1.3.3 Time evolution of spin states 1.3.4 Rotation of spin states 1.3.5 Rotation of a spin observation coordinate frame 1.4 Non-cloning principle for qbit 1.5 Quantum entanglement 1.5.1 What is entanglement? 1.5.2 Superposition and entanglement 1.6 Another example of qbit Reference CH002.pdf Chapter 2 Universal gates 2.1 Classical universal gates 2.2 Alternative universal gates 2.3 NOT, CNOT, CCNOT, and Fredkin gates using spin states 2.3.1 NOT-gate 2.3.2 CNOT-gate 2.3.3 CCNOT-gate (Toffoli gate) 2.3.4 Fredkin gate References CH003.pdf Chapter 3 Quantum logic gates 3.1 Introduction to quantum gate simulation—Blueqat for Python 3.1.1 Installation of Python and Blueqat 3.2 Quantum gates 3.2.1 Pauli’s spin matrices 3.2.2 Hadamard gate (H-gate) 3.2.3 Superposition of two qbits by applying an H-gate to each qbit 3.2.4 S-gate and T-gate 3.2.5 Rotational gates at arbitrary angles 3.3 Controlled-unitary (controlled-U) gates 3.3.1 CNOT (or CX) gate 3.3.2 Controlled-Z gate and controlled-P gate 3.3.3 Controlled–Z equivalent circuit 3.3.4 SWAP gate 3.3.5 CCNOT gate (Toffoli gate) 3.3.6 Bell gate 3.3.7 Reverse Bell (B−1) 3.3.8 GHZ state 3.4 Half adder from quantum gates References CH004.pdf Chapter 4 Algorithms of quantum computation 4.1 Deutsch’s algorithm 4.2 Grover’s algorithm 4.3 Quantum Fourier transform 4.3.1 Idea of quantum Fourier transform (QFT) [9] 4.3.2 QFT of orthogonal basis 4.3.3 Inverse quantum Fourier transform 4.4 Phase estimation 4.5 Shor’s algorithm for prime factorization 4.5.1 Periodicity of a number 4.5.2 Shor’s idea 4.5.3 Prime factorization of M=15 4.6 Simon’s algorithm 4.7 Error corrections 4.7.1 Bit flip error [14] 4.7.2 Phase flip error [15] References CH005.pdf Chapter 5 Quantum information: entanglement and teleportation 5.1 Bell’s inequality 5.1.1 Classical interpretation of entangled states 5.1.2 Quantum entanglement 5.2 Quantum teleportation 5.3 Superdense coding References CH006.pdf Chapter 6 Quantum cryptography (quantum key distribution) 6.1 Cryptography using a secret key 6.2 Photon-based qbit 6.3 BB84 protocol References APP.pdf Chapter A.1 Implementation of qbits A.2 Commercial quantum computers References