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

✍ Scribed by Shinil Cho

• Publisher: Iop Publishing Ltd
• Year: 2022
• Tongue: English
• Leaves: 108
• Category: Library

✦ Table of Contents

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