CONTENTS -- Preface -- Symposium -- List of Participants -- Organizing Committee -- Bosons in an Optical Lattice with a Synthetic Magnetic Field K. Kasamatsu -- 1. Introduction -- 2. Formulation -- 2.1. Bose-Hubbard model -- 2.2. Frustrated XY model -- 2.3. Hamiltonian for hard-core bosons in an effective magnetic field -- 2.3.1. CP1 variable and path-integral representation -- 3. Ground state -- 4. Phase structures at finite T -- 4.1. Density fluctuation -- 4.2. The finite temperature phase transition -- 4.2.1. f=0 -- 4.2.2. f=1/2 -- 4.2.3. f=2/5 -- 5. Summary -- Acknowledgments -- Appendix A. Reduction to the Josephson junction regime -- Appendix A.1. Determination of Jij -- Appendix A.2. Estimation of the parameters -- Appendix B. Relation between the CP1 model and the other models -- Appendix C. Symmetry of the gauged CP1 model -- References -- Quantum Simulation Using Exciton-Polaritons and their Applications Toward Accelerated Optimization Problem Search T. Byrnes, K. Yan, K. Kusudo, M. Fraser and Y. Yamamoto -- 1. Introduction -- 2. Quantum Simulation of the Hubbard Model -- 3. Exciton-Polaritons -- 4. Quantum Simulation with Exciton-Polaritons -- 4.1. Excited state condensation in one dimensional periodic lattice potentials -- 4.2. Mott transition of EPs and indirect excitons in a periodic potential -- 5. Accelerated Optimization Problem Search Using BECs -- 5.1. The bosonic Ising model -- 5.2. Performance of the bosonic Ising model -- 6. Summary and Conclusions -- Acknowledgments -- References -- Quantum Simulation Using Ultracold Atoms in Optical Lattices S. Sugawa, S. Taie, R. Yamazaki and Y. Takahashi -- 1. Introduction -- 1.1. Quantum simulation of Hubbard model -- 1.2. Why quantum simulation? -- 1.3. Extending the system -- 2. An approach using ytterbum -- 3. Production of quantum degenerate Yb atoms.

4. Superfluid-Mott insulator transition -- 5. Strongly-correlated phases in Bose-Fermi mixtures -- 5.1. Hamiltonian of the system -- 5.2. Repulsively interacting Bose-Fermi system -- 5.3. Attractively interacting Bose-Fermi system -- 5.4. Thermodynamics -- 6. Prospect -- Acknowledgement -- References -- Universality of Integrable Model: Baxter's T-Q Equation, SU(N)/SU(2)N-3 Correspondence and -Deformed Seiberg- Witten Prepotential T.-S. Tai -- 1. Introduction and summary -- 2. XXX spin chain -- 2.1. Baxter's T-Q equation -- 2.2. More detail -- 3. XXX Gaudin model -- 3.1. RHS of Fig. 3 -- 3.2. LHS of Fig. 3 -- 3.2.1. Free-field representation -- 4. Application and discussion -- 4.1. Discussion -- 4.2. XYZ Gaudin model -- Acknowledgments -- Appendix A -- Definition of wn -- References -- Exact Analysis of Correlation Functions of the XXZ Chain T. Deguchi, K. Motegi and J. Sato -- 1. Introduction -- 2. Spin-1/2 XXZ chain -- 3. Algebraic Bethe ansatz -- 4. Steps to calculate correlation functions -- 5. Integrable higher spin XXZ chain -- 6. Conclusion -- Acknowledgments -- Appendix A: Evaluation of (42) -- References -- Classical Analogue of Weak Value in Stochastic Process H. Tomita -- 1. Introduction -- 2. Self-adjoint form of stochastic master equation -- 3. Two-time conditional probability -- 4. Stochastic model of classical Ising spins -- 5. Extension of TTCP to a density matrix -- 6. Summary and discussions -- Acknowledgment -- References -- Scaling of Entanglement Entropy and Hyperbolic Geometry H. Matsueda -- 1. Introduction -- 2. Entanglement Entropy and Singular Value Decomposition -- 3. Scaling of Entanglement Entropy -- 3.1. Historical roots of anomalous entropy scaling -- 3.2. General coodinate transformation and horizon -- 3.3. Area law and its logarithmic violation at criticality -- 3.4. Fermi surfaces and entropy.

3.5. Topological entanglement entropy -- 3.6. Entanglement support of matrix product state -- 4. Holographic Entanglement Entropy: Connection between Scaling and Hyperbolic Geometry -- 4.1. Anti-de Sitter space -- 4.2. Killing equation and conformal invariance -- 4.3. Geometric interpretation of entanglement entropy -- 5. Tensor Networks and Extra Dimension -- 5.1. From matrix product to tensor product -- 5.2. Tree tensor networks and multiscale entanglement renormalization ansatz: Hierarchical tensor network -- 6. Compactification and Entropy -- 6.1. Bulk/edge correspondence and compactification -- 6.2. Field theory with extra dimension -- 6.3. VBS/CFT correspondence -- 6.4. Suzuki-Trotter decomposition -- 6.5. Entropy scaling, quantum-classical correspondence, and hyperbolic geometry hidden in image processing based on SVD -- 7. Summary -- References -- From Classical Neural Networks to Quantum Neural Networks B. Tirozzi -- 1. The Hopfield model -- 2. Estimates of the observables for quantum spin systems -- 3. Multi-qubit systems and quantum neural networks -- 4. Estimates of the ground state energy of classical neural networks -- 4.1. Ising ferromagnetic model -- 4.2. Hopfield model with a finite number of patterns -- 4.3. Hopfield model with finite capacity -- 4.4. Quantum neural networks -- 5. Experiments and Simulations -- 5.1. Experiment -- 5.2. Simulations -- 6. Open Problems -- References -- Analysis of Quantum Monte Carlo Dynamics in Infinite-range Ising Spin Systems: Theory and Its Possible Applications J. Inoue -- 1. Introduction -- 2. The model system and formulation -- 2.1. The Glauber dynamics and its transition probability -- 2.2. The master equation -- 2.3. From master equation to deterministic flows -- 2.3.1. The static approximation -- 2.3.2. Classical limit -- 2.4. Dynamics and steady state.

2.5. On the validity of static approximation -- 3. The quantum Hopfield model -- 3.1. The classical system -- 3.2. The quantum system -- 3.2.1. The master equation -- 3.2.2. The classical and zero-temperature limits -- 3.3. Limit cycle solution for asymmetric connections -- 3.3.1. Result for just only two embedded patterns -- 4. Image restoration -- 5. Concluding remarks -- Acknowledgement -- References -- A Method to Control Order of Phase Transition: Invisible States in Discrete Spin Models R. Tamura, S. Tanaka and N. Kawashima -- 1. Introduction -- 2. Nature of the Phase Transition -- 3. Preceding Models -- 3.1. Blume-Capel model -- 3.2. Wajnflasz-Pick model -- 4. Potts Model with Invisible States -- 4.1. Mean-field analysis -- 4.2. Monte Carlo simulation -- 4.3. Another representation of the Potts model with invisible states -- 5. Conclusion and Future Perspective -- Acknowledgements -- References -- Quantum Annealing and Quantum Fluctuation Effect in Frustrated Ising Systems S. Tanaka and R. Tamura -- 1. Introduction -- 2. Implementation Methods of Quantum Annealing -- 2.1. Quantum Monte Carlo method -- 2.2. Real-time dynamics -- 3. Quantum Field Response of Frustrated Ising Systems -- 3.1. Order by disorder effect in fully frustrated systems -- 3.2. Decorated bond systems -- 4. Conclusion and Future Perspective -- Acknowledgement -- References.