前半(渡邉 担当分)
Introduction to non-perturbative methods in condensed matter physics
- Symmetries in condensed matter physics
- "Bloch theorem" for spontaneous current
- Various kinds of "LSM theorem"
- Spontaneous symmetry breaking and Nambu-Goldstone bosons
- Thouless pump, polarization, and the Chern number in many-body systems
- "Symmetry indicator" of topology
後半(江澤 担当分)
1. Universal quantum computations
1.1 Qubits and quantum gates
1.2 Hadamard, phase-shift and CNOT gates
1.3 SWAP, CZ, Toffoli and Fredkin gates
1.4 Solovay-Kitaev theorem
1.5 Clifford gates and Gottesman-Knill theorem
1.6 Quantum circuits
2. Quantum entanglement
2.1 Bell states
2.2 Singlet state
2.3 W state
2.4 Greenberger-Horne-Zeilinger state
3. Quantum algorithm
3.1 Hadamard test
3.2 Kitaev phase estimation algorithm
3.3 Quantum Fourier transformation
3.4 Harrow-Hassidim-Lloyd algorithm
4. Machine learning
4.1 Artificial neuron and neural network
4.2 Support Vector Machine
4.3 Linear regression
4.4 Singular Value Decomposition
4.5 Principal Component Analysis
5. Quantum machine learning
5.1 Quantum neuron
5.2 Quantum Variational Eigensolver
5.3 Quantum Approximate Optimization Algorithm
5.4 Quantum Circuit Learning
5.5 Quantum Support Vector Machine
5.6 Quantum Linear Regression