05513nam 2200673Ia 450 991046479470332120200520144314.0981-4425-19-2(CKB)3400000000087241(EBL)1080988(OCoLC)821180536(SSID)ssj0000916934(PQKBManifestationID)11562474(PQKBTitleCode)TC0000916934(PQKBWorkID)10877958(PQKB)11067496(MiAaPQ)EBC1080988(WSP)00002826(Au-PeEL)EBL1080988(CaPaEBR)ebr10627503(CaONFJC)MIL498493(EXLCZ)99340000000008724120121210d2013 uy 0engurbuu|||uu|||txtccrLectures on quantum computing, thermodynamics and statistical physics[electronic resource] /editors, Mikio Nakahara, Shu TanakaSingapore ;Hackensack, NJ World Scientific Pub.c20131 online resource (199 p.)Kinki University series on quantum computing ;vol. 8Description based upon print version of record.981-4425-18-4 Includes bibliographical references.Preface; CONTENTS; Quantum Annealing: From Viewpoints of Statistical Physics, Condensed Matter Physics, and Computational Physics Shu Tanaka and Ryo Tamura; 1. Introduction; 2. Ising Model; 2.1. Magnetic Systems; 2.2. Nuclear Magnetic Resonance; 3. Implementation Methods of Quantum Annealing; 3.1. Monte Carlo Method; 3.2. Deterministic Method Based on Mean-Field Approximation; 3.3. Real-Time Dynamics; 3.4. Experiments; 4. Optimization Problems; 4.1. Traveling Salesman Problem; 4.1.1. Monte Carlo Method; 4.1.2. Quantum Annealing; 4.1.3. Comparison with Simulated Annealing and Quantum Annealing4.2. Clustering Problem 5. Relationship between Quantum Annealing and Statistical Physics; 5.1. Kibble-Zurek Mechanism; 5.1.1. Efficiency of Simulated Annealing and Quantum Annealing; 5.1.2. Simulated Annealing for Random Ferromagnetic Ising Chain; 5.1.3. Quantum Annealing for Random Ferromagnetic Ising Chain; 5.1.4. Comparison between Simulated and Quantum Annealing Methods; 5.2. Frustration Effects for Simulated Annealing and Quantum Annealing; 5.2.1. Thermal Fluctuation and Quantum Fluctuation Effect of Geometrical Frustrated Systems5.2.2. Non-Monotonic Behavior of Correlation Function in Decorated Bond System 6. Conclusion; Acknowledgement; References; Spin Glass: A Bridge between Quantum Computation and Statistical Mechanics Masayuki Ohzeki; 1. Introduction: Statistical Mechanics and Quantum Mechanics; 2. Training: Statistical Mechanics; 2.1. Student's misreading point: Probability is...; 2.2. Probability describes... a certain behavior; 2.3. Large deviation property; 2.4. Mean-field analysis; 2.5. Phase transition; 2.6. Spin glasses; 2.7. Gauge theory; 3. Quantum Error Correction: Surface Code; 3.1. Error model3.2. Surface code 3.2.1. Check operators and error syndrome; 3.2.2. Probability of error chains; 3.3. Analyses on accuracy thresholds for surface code; 3.3.1. Duality analysis: Simple case; 3.3.2. Duality analysis: Spin glass; 3.3.3. Duality analysis with real-space renormalization; 3.3.4. Other cases; 3.3.5. Depolarizing channel; 4. Quantum Annealing and Beyond; 4.1. Quantum adiabatic computation: Short review; 4.2. Novel type of quantum annealing; 4.2.1. Classical quantum mapping; 4.2.2. Jarzynski equality; 4.2.3. Quantum Jarzynski annealing; 4.2.4. Problems in measurement of answer4.3. Non-adiabatic quantum computation 4.3.1. Jarzynski equality for quantum system; 4.3.2. Performance of non-adiabatic quantum annealing; 4.4. Analyses on non-adiabatic quantum annealing; 4.4.1. Gauge transformation for quantum spin systems; 4.4.2. Relationship between two different paths of NQA; 4.4.3. Exact relations involving inverse statistics; 5. Summary; References; Second Law-like Inequalities with Quantum Relative Entropy: An Introduction Takahiro Sagawa; 1. Introduction; 2. Quantum States and Dynamics; 2.1. Quantum States and Observables; 2.2. Quantum Dynamics2.2.1. Unitary EvolutionThis book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notKinki University series on quantum computing ;v. 8.Statistical physicsThermodynamicsElectronic books.Statistical physics.Thermodynamics.004.1530.12Nakahara Mikio52615Tanaka Shu971675MiAaPQMiAaPQMiAaPQBOOK9910464794703321Lectures on quantum computing, thermodynamics and statistical physics2209202UNINA