محاسبات کوانتومی، پیچیدگی و فیزیک چندجسمی

Introduction......Page 12 Simulations of Physics with Quantum Computers......Page 20 The Conventional Model of Quantum Computation......Page 22 Hamiltonian Evolutions......Page 28 Controlled Operations......Page 29 Deterministic Quantum Algorithms......Page 31 One-Ancilla Qubit Measurement Processes......Page 32 Quantum Algorithms and Quantum Simulations......Page 33 Simulations of Fermionic Systems......Page 36 Simulations of Anyonic Systems......Page 41 Simulations of Bosonic Systems......Page 42 Applications: The 2D fermionic Hubbard model......Page 48 Quantum Algorithms: Efficiency and Errors......Page 50 Liquid-State NMR Quantum Information Processor......Page 53 Applications: The Fano-Anderson Model......Page 57 Experimental Protocol and Results......Page 62 Summary......Page 65 Quantum Entanglement as an Observer-Dependent Concept......Page 70 Quantum Entanglement......Page 74 Separability and von Neuman Entropy......Page 75 Mixed-State Entanglement and the Concurrence......Page 77 Measures of Quantum Entanglement......Page 78 Generalized Entanglement: Definition......Page 79 Generalized Entanglement and Lie Algebras......Page 80 Generalized Entanglement and Mixed States......Page 84 Two-Spin Systems......Page 85 N-Spin Systems......Page 89 Fermionic Systems......Page 90 Summary......Page 92 Generalized Entanglement as a Resource in Quantum Information......Page 94 Quantum Cryptography......Page 95 Quantum Teleportation......Page 97 Quantum Entanglement and Quantum Computation......Page 98 Efficient Classical Simulations of Quantum Physics......Page 102 Higher Order Correlations......Page 106 Generalized Entanglement and Quantum Computation......Page 108 Efficient Initial State Preparation......Page 109 Summary......Page 111 Generalized Entanglement and Many-Body Physics......Page 112 Entanglement and Quantum Phase Transitions......Page 113 Lipkin-Meshkov-Glick Model......Page 115 Anisotropic XY Model in a Transverse Magnetic Field......Page 121 General Mean-Field Hamiltonians......Page 131 Diagonalization Procedure......Page 133 Example: Fermionic Systems......Page 138 Summary......Page 139 Conclusions......Page 140 Future Directions......Page 144 Discrete Fourier Transforms......Page 146 Discrete Fourier Transform and Propagation of Errors......Page 148 The Adjoint Representation......Page 150 Separability, Generalized Unentanglement, and Local Purities......Page 154 Approximations of the exponential matrix......Page 158 Scaling of the Method......Page 162 Efficient Classical Evaluation of High-Order Correlation Functions......Page 164 Classical Limit in the LMG Model......Page 170