Physics, Mathematics, and All That Quantum Jazz: Proceedings of the Summer Workshop, Kinki University, Osaka, Japan 7 9 August 2013

Proceedings of the Summer Workshop, Kinki University, Osaka, Japan 7-9 August 2013 This book is a collection of contributions from a Summer Workshop on Physics, Mathematics, and All That Quantum Jazz . Subjects of the symposium include quantum information theory, quantum annealing, Bose gases, and thermodynamics from a viewpoint of quantum physics. Contributions to this book are prepared in a self-contained manner so that readers with a modest background may understand the subjects CONTENTS 8 Preface 6 Summer Workshop on Physics, Mathematics, and All That Quantum Jazz 12 LIST OF PARTICIPANTS 16 My Life as a Quantum Physicist 22 1. My Research Career to Date 22 2. Future Prospects 27 Acknowledgments 28 References 28 A Review on Operator Quantum Error Correction — Dedicated to Professor Mikio Nakahara on the Occasion of His 60th Birthday 34 1. Introduction 34 2. General mathematical framework 35 2.1. Quantum error correcting code 35 2.2. Decoherence free subspace and noiseless subsystem 37 2.3. Operator quantum error correction 37 3. Collective noise 38 Acknowledgment 41 References 41 Implementing Measurement Operators in Linear Optical and Solid-State Qubits 48 1. Introduction 48 2. Setting 50 3. Design of general measurements on linear optical qubits 51 3.1. Symmetric arbitrary-strength two-outcome measurements 51 3.2. General two-outcome measurements 55 3.3. General multi-outcome measurements 57 4. Solid-state qubits 58 5. Summary 60 Acknowledgments 60 References 60 Fast and Accurate Simulation of Quantum Computing by Multi-Precision MPS: Recent Development 66 1. Introduction 66 2. Basics of the TDMPS method 68 2.1. Operator-space TDMPS 70 3. Necessity of multiprecision computation 71 4. Performance 72 4.1. Recent speedup in Hermitian-matrix diagonalization 72 4.2. Simulation of the Deutsch-Jozsa algorithm 73 4.3. Simulation of the Grover search 75 4.4. Simulation of a QFT-based in-place addition 77 4.5. Simulation of the Shor’s algorithm 80 5. Concluding remarks 82 Acknowledgments 83 References 83 Entanglement Properties of a Quantum Lattice-Gas Model on Square and Triangular Ladders 88 1. Introduction 89 2. Model 91 3. Reduced density matrix 94 4. Entanglement properties 97 4.1. Entanglement entropy 97 4.2. Entanglement spectrum 99 4.3. Nested entanglement entropy 99 5. Summary and future perspective 100 Acknowledgments 101 Appendix A. Critical phenomena of the classical hard-square model 101 References 103 On Signal Amplification from Weak-Value Amplification 108 1. Introduction 108 2. What is Probability in Quantum Mechanics? 109 3. Extended Probability Theory via Two-State Vector Formalism 112 4. Signal Amplification 114 Acknowledgments 116 References 116 Topological Protection of Quantum Information 120 1. Introduction 120 2. Planer surface code and defect qubits 121 3. Topological quantum computation by braiding 125 4. Topological error correction and threshold values 127 5. Topologically protected MBQC 128 6. Applications 132 7. Conclusion 134 Acknowledgments 134 References 134 Quantum Annealing with Antiferromagnetic Fluctuations for Mean-Field Models 138 1. Introduction 138 2. Quantum annealing 141 3. The ferromagnetic p-spin model 142 4. The Hopfield model 143 5. Summary and conclusion 146 Acknowledgments 147 References 147 A Method to Change Phase Transition Nature — Toward Annealing Methods 152 1. Introduction 152 2. Optimization problems 154 3. Annealing methods 156 3.1. Mechanism of simulated annealing 157 3.2. Mechanism of quantum annealing 160 4. Phase transitions 162 4.1. First-order phase transition 163 4.2. Second-order phase transition 164 5. Potts model with invisible states 165 6. Conclusion and future perspective 170 Acknowledgments 171 Appendix A. Monte Carlo method 172 Appendix B. Real-time dynamics by Schrodinger equation 173 References 174 Computational Analysis of the First Stage of the Photosynthetic System, the Light-Dependent Reaction, by Quantum Chemical Simulation Method 182 1. Introduction 182 2. Calculation Methods 183 3. Results and Discussions 185 4. Conclusion 190 References 191 Two-Qubit Gate Operation on Selected Nearest Neighboring Qubits in a Neutral Atom Quantum Computer 192 References 193 A Simple Operator Quantum Error Correction Scheme Avoiding Fully Correlated Errors 196 1. Introduction 196 2. Operator Quantum Error Correction 197 3. Simplest NS Under Fully Correlated Noise 198 4. Experiments 199 5. Conclusions 200 References 200 Black Hole Predictability, Classical and Quantum 204 1. Introduction 204 2. Black hole thermodynamics 205 3. Breakdown of predictability 205 4. Resolution to the information puzzle 206 5. Summary 208 Acknowledgments 208 References 208 Classical Field Simulation of Finite-Temperature Bose Gases 212 1. Introduction 212 2. Model and Method 213 3. Results 215 4. Summary 218 Acknowledgment 218 References 219 Atomic Quantum Simulations of Lattice Gauge Theory: Effect of Gauge Symmetry Breaking 224 1. Introduction 224 2. U(1) pure lattice gauge theory 225 3. Atomic quantum simulators of U(1) lattice gauge theory 227 4. Implementation of U(1) gauge-Higgs model 232 5. Summary and discussion 234 References 235 Recursive Construction of Noiseless Subsystem for Qudits 240 1. Introduction 240 2. The recursive scheme for qubits 242 3. General case: recursive construction of noiseless subsystem for qudits 245 4. Concluding remarks 248 Acknowledgments 249 References 249 Composite Quantum Gates for Precise Quantum Control 254 Acknowledgments 258 References 258 New Formulation of Statistical Mechanics Using Thermal Pure Quantum States 262 1. Introduction 262 2. Canonical TPQ State 263 3. Thermodynamic Functions and Genuine Thermodynamic Variables 264 4. Mechanical Variables 265 5. A Numerical Application 266 6. Microcanonical TPQ State 267 7. Expansion of the Canonical TPQ State 268 8. Quantum and Thermal Fluctuations 269 9. Entanglement 271 10. Conclusion 272 References 273 Thermodynamics in Unitary Time Evolution 276 1. Introduction 276 2. Basic Concepts 277 2.1. Typicality 277 2.2. Equilibration 278 2.2.1. Motivation 278 2.2.2. Assumptions 279 2.2.3. Theory of equilibration 280 3. Thermalization 281 3.1. Eigenstate Thermalization Hypothesis (ETH) 281 3.2. Other Two Scenarios 282 3.2.1. Typicality argument 282 3.2.2. Eigenstate Randomization Hypothesis (ERH) 283 4. Finite-Size Scaling Analysis of the ETH 284 5. Discussion 286 6. Prospect 286 Acknowledgments 287 References 287 Second Law of Thermodynamics with QC-Mutual Information 290 References 290 My life as a quantum physicist / M. Nakahara -- A review on operator quantum error correction - Dedicated to Professor Mikio Nakahara on the occasion of his 60th birthday / C.-K. Li, Y.-T. Poon and N.-S. Sze -- Implementing measurement operators in linear optical and solid-state qubits / Y. Ota, S. Ashhab and F. Nori -- Fast and accurate simulation of quantum computing by multi-precision MPS: Recent development / A. Saitoh -- Entanglement properties of a quantum lattice-gas model on square and triangular ladders / S. Tanaka, R. Tamura and H. Katsura -- On signal amplification from weak-value amplification / Y. Shikano -- Topological protection of quantum information / K. Fujii -- Quantum annealing with antiferromagnetic fluctuations for mean-field models / Y. Seki and H. Nishimori -- A method to change phase transition nature - Toward annealing methods / R. Tamura and S. Tanaka -- Computational analysis of the first stage of the photosynthetic system, the light-dependent reaction, by quantum chemical simulation method / M. Tada-Umezaki -- Two-qubit gate operation on selected nearest neighboring qubits in a neutral atom quantum computer / E. Hosseini Lapasar [und weitere] -- A simple operator quantum error correction scheme avoiding fully correlated errors / C. Bagnasco, Y. Kondo and M. Nakahara -- Black hole predictability, classical and quantum / A. Ishibashi -- Classical field simulation of finite-temperature Bose gases / T. Sato -- Atomic quantum simulations of lattice gauge theory: Effect of gauge symmetry breaking / K. Kasamatsu, I. Ichinose and T. Matsui -- Recursive construction of noiseless subsystem for qudits / U. Gungordu [und weitere] -- Composite quantum gates for precise quantum control / M. Bando [und weitere] -- New formulation of statistical mechanics using thermal pure quantum states / S. Sugiura and A. Shimizu -- Thermodynamics in unitary time evolution / T.N. Ikeda -- Second law of thermodynamics with QC-mutual information / T. Sagawa