量子物理学

前半６回（平山　担当分） 1. Ab initio Calculation 1.1 Density functional theory 1.2 Band structure 1.3 Effective model 2. Topology in Crystals 2.1 topology in real space 2.2 topology in k space 2.3 Berry phase and Zak phase 3. Topological Materials (Insulator) 3.1 Quantum spin Hall effect 3.2 3D Topological insulator 3.3 Quantum anomalous insulator 4. Topological Materials (Semimetal) 4.1 Weyl semimetal 4.2 Dirac semimetal 4.3 Nodal-line semimetal 5. Strong Correlation 5.1 Correlation in ab initio calculation 5.2 Many body Hamiltonian 5.3 Strongly correlated systems 6. Exotic Materials 6.1 Correlation in topology 6.2 Topological superconductivity 6.3 Other materials 後半６回（江澤　担当分） 1. Quantum computer 　　1.1 Noisy Intermediate Scale Quantum device (NISQ) and Fault Tolerant Quantum Computer (FTQC) 　　1.2 Qubits and Quantum Gates 　　1.3 the Pauli gates, the Hadamard gate and the CNOT gate 　　1.4 Quantum Circuits 　　1.5 Universal quantum computation and Solovay-Kitaev theorem 　　 2. Classical error correction 　　2.1 repetition codes 　　2.2 Generator matrix and parity-check matrix 　　2.3 Hamming code 　　 3. Quantum error correction 　　3.1 No cloning theorem 　　3.2 Bit flip error correction code 　　3.3 Phase flip error correction code 　　3.4 Shor code 　　3.5 Stabilizer code 　　3.6 Calderbank-Shor-Steane code 　　3.7 Steane code 　　3.8 Transversality 　　3.9 threshold theorem 　　3.10 Fault Tolerant Quantum Computation 4. Quantum electronics 　　4.1 charge, current and equation of continuity 　　4.2 Noether theorem 　　4.3 spin and spin current 　　4.4 sd exchange interaction 　　4.5 spin-orbitinteraction 　　4.6 local gauge transformation and covariant derivative 5. Quantum magnets 　　5.1 Heisenberg model 　　5.2 XX quantum spin chain 　　5.3 Jordan-Wigner transformation 　　5.4 Holstein--Primakoff transformation 　　5.5 Magnon in ferromagnets 　　5.6 Magnon in antiferromagnets 　　5.7 Bogoliubov transfomation 　　 6. Quantum spintronics 　　6.1 exchange spin current 　　6.2 spin-wave spin current 　　6.3 nonequilibrium green function

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