Preface |
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Author biography |
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Acknowledgments |
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xii | |
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1 Two-level quantum systems |
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1 | (1) |
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1 | (3) |
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1.1.1 Calculation rules of vectors and matrices |
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1 | (3) |
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1.1.2 Combining two different vector spaces---direct product |
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4 | (1) |
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1.2 Foundation of quantum mechanics |
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4 | (2) |
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1.2.1 General properties of quantum states |
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4 | (2) |
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1.3 Quantum state vectors |
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6 | (5) |
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1.3.1 Two-level quantum state vector: qbit |
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6 | (1) |
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1.3.2 Projection operators for spin states |
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7 | (1) |
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1.3.3 Time evolution of spin states |
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8 | (1) |
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1.3.4 Rotation of spin states |
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8 | (2) |
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1.3.5 Rotation of a spin observation coordinate frame |
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10 | (1) |
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1.4 Non-cloning principle for qbit |
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11 | (1) |
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11 | (2) |
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1.5.1 What is entanglement? |
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11 | (1) |
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1.5.2 Superposition and entanglement |
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12 | (1) |
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1.6 Another example of qbit |
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13 | (1) |
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14 | |
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1 | (1) |
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2.1 Classical universal gates |
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1 | (1) |
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2.2 Alternative universal gates |
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2 | (1) |
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2.3 NOT, CNOT, CCNOT, and Fredkin gates using spin states |
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3 | (1) |
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3 | (1) |
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4 | (1) |
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2.3.3 CCNOT-gate (Toffoli gate) |
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5 | (1) |
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6 | (2) |
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8 | |
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1 | (1) |
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3.1 Introduction to quantum gate simulation---Blueqat for Python |
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1 | (2) |
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3.1.1 Installation of Python and Blueqat |
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1 | (2) |
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3 | (7) |
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3.2.1 Pauli's spin matrices |
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3 | (2) |
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3.2.2 Hadamard gate (H-gate) |
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5 | (1) |
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3.2.3 Superposition of two qbits by applying an H-gate to each qbit |
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6 | (2) |
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8 | (1) |
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3.2.5 Rotational gates at arbitrary angles |
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8 | (2) |
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3.3 Controlled-unitary (controlled-U) gates |
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10 | (8) |
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10 | (1) |
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3.3.2 Controlled-Z gate and controlled-P gate |
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10 | (2) |
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3.3.3 Controlled-Z equivalent circuit |
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12 | (1) |
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13 | (1) |
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3.3.5 CCNOT gate (Toffoli gate) |
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14 | (1) |
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15 | (1) |
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16 | (1) |
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17 | (1) |
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3.4 Half adder from quantum gates |
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18 | (2) |
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4 Algorithms of quantum computation |
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1 | (1) |
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1 | (4) |
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5 | (3) |
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4.3 Quantum Fourier transform |
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8 | (7) |
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4.3.1 Idea of quantum Fourier transform (QFT) |
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8 | (2) |
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4.3.2 QFT of orthogonal basis |
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10 | (4) |
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4.3.3 Inverse quantum Fourier transform |
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14 | (1) |
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15 | (2) |
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4.5 Shor's algorithm for prime factorization |
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17 | (5) |
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4.5.1 Periodicity of a number |
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17 | (1) |
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18 | (3) |
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4.5.3 Prime factorization of M=15 |
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21 | (1) |
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22 | (4) |
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26 | (1) |
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26 | (2) |
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28 | (4) |
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32 | |
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5 Quantum information: entanglement and teleportation |
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1 | (1) |
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2 | (5) |
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5.1.1 Classical interpretation of entangled states |
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2 | (1) |
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5.1.2 Quantum entanglement |
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2 | (5) |
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5.2 Quantum teleportation |
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7 | (2) |
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9 | (2) |
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6 Quantum cryptography (quantum key distribution) |
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1 | (1) |
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6.1 Cryptography using a secret key |
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1 | (1) |
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2 | (1) |
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3 | (3) |
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Appendix A Commercial quantum computers |
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