درهم‌تنیدگی، انتقال فاز کوانتومی و الگوریتم‌های کوانتومی

Introduction......Page 19 Majorization along parameter and renormalization group flows......Page 29 Global, monotonous and fine-grained entanglement loss......Page 31 Majorization along parameter flows in (1+1)-dimensional quantum systems......Page 32 Quantum Heisenberg spin chain with a boundary......Page 36 Quantum XY spin chain with a boundary......Page 37 Critical quantum XX spin chain with a boundary......Page 40 Conclusions of Chapter 1......Page 42 Single-copy entanglement in (1+1)-dimensional quantum systems......Page 43 Operational definition of the single-copy entanglement......Page 44 Exact conformal field theoretical computation......Page 46 Exact computation in quasi-free fermionic quantum spin chains......Page 47 Single-copy entanglement away from criticality......Page 51 Conclusions of Chapter 2......Page 52 Entanglement entropy in the Lipkin-Meshkov-Glick model......Page 55 The Lipkin-Meshkov-Glick model......Page 56 Entanglement within different regimes......Page 57 Analytical study of the isotropic case......Page 58 Numerical study of the anisotropic case......Page 60 Comparison to quantum spin chains......Page 61 Conclusions of Chapter 3......Page 64 Entanglement entropy in quantum algorithms......Page 65 The factoring quantum algorithm......Page 67 Analytical results......Page 69 The adiabatic quantum algorithm......Page 70 Exact Cover......Page 71 Numerical results up to 20 qubits......Page 73 Entanglement in adiabatic quantum searching algorithms......Page 81 Analytical results......Page 83 Conclusions of Chapter 4......Page 88 Classical simulation of quantum algorithms using matrix product states......Page 91 The matrix product state ansatz......Page 92 Computing dynamics......Page 96 Classical simulation of an adiabatic quantum algorithm solving Exact Cover......Page 101 Discretization of the continuous time evolution in unitary gates......Page 102 Numerical results of a simulation with matrix product states......Page 103 Conclusions of Chapter 5......Page 109 Majorization arrow in quantum algorithm design......Page 111 Applying majorization theory to quantum algorithms......Page 112 Majorization in quantum phase-estimation algorithms......Page 113 The quantum phase-estimation algorithm......Page 114 Analytical results......Page 115 Natural majorization and comparison with quantum searching......Page 122 The quantum hidden affine function determination algorithm......Page 123 Majorization in adiabatic quantum searching algorithms......Page 125 Numerical results......Page 126 Majorization in a quantum walk algorithm with exponential speed-up......Page 130 The exponentially fast quantum walk algorithm......Page 131 Numerical results......Page 133 Conclusions of Chapter 6......Page 135 General conclusions and outlook......Page 139 Majorization......Page 141 Some notions about conformal field theory......Page 143 Some notions about classical complexity theory......Page 147