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招待講演等(Invited Talks, Proceedings)
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１．トポロジカル原子層物質：
２．バレートロニクス：
３．ディラック電子系：
４．スカーミオン：
５．高次トポロジカル絶縁体：
６．量子コンピュータと量子機械学習：
大学院講義
Quantum Physics 2024
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 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 and spintronics
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
4.7 Exchange spin current
4.8 Spin-wave spin current
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. Nonequilibrium Green function
6.1 time-ordered product
6.2 lesser, greater and Keldysh Green function
6.3 Langreth’s theorem
6.4 Green function for free fermions
6.5 spectral function
6.6 Landauer formula
Quantum Physics 2023
1. Quantum optics
1.1 Quantization of electromagnetic field
1.2 boson and photon
1.3 Many bosons
1.4 Baker-Campbell-Hausdorff formula
1.5 Coherent state
1.5.1 quantum fluctuation
1.5.2 Number operator and phase operator
1.5.3 Hamiltonian for coherent states
1.5.4 su(2) and su(1,1) algebra
1.5.5 su(2) algebra of photon
1.5.6 cat states
1.6 Squeezing
1.6.1 Bogoliubov transformation of bosons
1.6.2 Interaction picture
1.6.3 Hamiltonian for squeezed states
1.6.4 Parametric down conversion
1.6.5 Four-wave mixing
1.6.6 Squeezed vacuum state
1.6.7 Quadrature squeezing
1.6.8 Squeezed coherent state
1.6.9 Amplitude squeezing
1.6.10 Phase squeezing
1.6.12 Degenerate parametric amplifier
1.6.13 Schwinger boson
1.6.15 su(1,1) algebra of distinguishable photon
1.6.16 Two-mode squeezed states
1.6.17 Two-mode squeezed vacuum states
1.6.18 Quadrature squeezing
1.6.19 Hamiltonian for the two-mode squeezed state
1.6.20 Non-degenerate parametric amplifier
1.6.21 fluctuation
1.6.22 Frequency up-converter
1.7 NOON state
1.8 Beam splitter
1.9 Balanced homodyne measurement
1.10 Photonic qubit
1.10.1 Fock qubit
1.10.2 Polarization qubit
1.10.3 Cat qubit
2. Open quantum system
2.1 Density operator, pure states and mixed states
2.2 von Neumann equation
2.3 Kraus operator
2.4 Projective measurement
2.5 Positive Operator Valued Measure (POVM)
2.6 Lindblad equation
2.7 Spontaneous emission
2.8 Relaxation
2.9 Dephasing
3. Cavity QED
3.1 Rabi Hamiltonian
3.2 Jaynes-Cummings Hamiltonian
4 Quantum computation
4.1 Qubit
4.2 One-qubit gates
4.2.1 Hadmard gate
4.2.2 Phase-shift gate
4.3 Two-qubit gates
4.3.1 CNOT gate
4.3.2 SWAP gate
4.3.3 CZ gate
4.4 Solovay-Kitaev theorem and universal quantum computation
4.5 No cloning theorem
5 Floquet theory
5.1 Bloch’s theorem
5.2 Floquet’s theorem
5.3 Floquet expansion
5.4 High-frequency perturbation theory
5.5 Photo-induced Dirac mass
Quantum Physics 2022
1. Topological soliton
1.1 Domain wall
1.2 Vortex
1.3 Skyrmion
1.4 Meron
1.5 Other topological soliton
2. Topological insulators
2.1 Su-Schrieffer-Heeger model
2.1.1 Bulk spectrum
2.1.2 Edge states and bulk-edge correspondence
2.1.3 Chiral symmetry
2.1.4 Chiral index of the SSH model
2.1.5 Dirac theory of the SSH model and Jackiw-Rebbi solution
3. Higher-order topological insulators
3.1 Corner and hinge states
3.2 Breathing Kagome model
4. Non-Hermitian topological systems
4.1 Nonreciprocity and Hatano-Nelson model
4.1.1 Non-Hermitian Skin states
4.2 Non-Hermitian SSH model with PT symmetry
5. Artifical topological systems
5.1 Mechanical systems
5.2 Electric circuits
5.3 Photonic systems
6. Superconducting qubit
6.1 Classical LC resonator
6.2 Quantum LC resonator
6.3 Superconducting qubit
6.4 Circuit Quantum Electrodynamics
6.5 Rabi model
6.6 Campbell-Baker-Hausdorff formula
6.7 Rotational-wave approximation
6.8 Jaynes-Cummings model
6.9 Schrieffer-Wolff transformation and quantum nondemolition measurement
6.10 Rabi oscillation
7. Quantum gates and quantum computation
7.1 Pauli X gate
7.2 Pauli Y gate
7.3 Phase-shift gate
7.4 Pauli Z gate
7.5 Hadamard gate
7.6 Capacitive coupling of two transmon qubits
7.7 iSWAP gate
7.8 CNOT gate
7.9 SWAP gate
7.10 Solovay-Kitaev theorem and universal quantum computation
Quantum Physics 2021
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 state
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
6. Quantum Random Access Memory (QRAM)
6.1 Basis encoding
6.2 Amplitude encoding
6.3 Matrix encoding
7. Non-Hermitian quantum mechanics
7.1 PT symetry
8. Open quantum mechanics
8.1 Lindblad master equation
8.2 Larmor precession
8.3 Superoperator
Quantum Physics 2020
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 state
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 Euler's theorem
3.5 Period-finding subroutine (Simon's algorithm)
3.6 Shor's algorithm
3.7 Grover's algorithm
4. Majorana fermions and topological quantum computations
4.1 Fermions and two Majorana fermions
4.2 Braiding of Majorana fermions and topological quantum computations
Quantum Physics 2019
1. Majorana fermions and topological quantum computations
1.1 Fermions and two Majorana fermions
1.2 Artin braid group
1.3 Three Majorana fermions, quaternion group and Pauli matrices
1.4 Four Majorana fermions and braiding
1.5 Non-Abelian anyon, ising anyon and fusion rule
2. Majorana fermions and topological superconductors
2.1 Particle-hole symmetry
2.2 Bogoliubov-de Gennes equation
2.3 Kitaev p-wave superconductor model
2.4 p+ip-wave topological superconductor model
2.5 He^3 B phase: topological superfluid
Quantum Physics 2018
1. DIRAC
THEORY
2.
SU-SCHRIEFFER-HEEGER MODEL
2.1
Jackiw-Rebbi solution
3. HONEYCOMB
DIRAC SYSTEM
3.1 Berry connection, Berry phase and Berry curvature
3.2 Hellmann-Feynman theorem
3.3
Thouless-Kohmoto-Nightingale-Nijs formula
3.4 Pontryagin number and Chern number
3.5 QHE in
the honeycomb system
3.6 Haldane
model and Kane-Mele model
4. MAJORANA
FERMION
4.1 Kitaev p-wave topological superconductor model
4.2 Z 2 topological invariant
4.3 Spinless p+ip-wave topological superconductor model
5. WEYL
SEMIMETAL
5.1 Monopole
charge
5.2 Weyl
semimetal, Chern number and anomalous Hall effects
5.3 Fermi arc
5.4 Weyl semimetal from Dirac semimetal with magnetic field
6. KITAEV SPIN LIQUID
Quantum Physics 2017
1
Ferromagnets and nonlinear sigma model
1.1 Exchange Interaction
1.2 Nonlinear sigma model from lattice model
2 Domain
Wall
2.1 One-dimensional soliton equation
2.2 Kinks and anti-kinks
2.3 Sine-Gordon Solitons and Jacobian Elliptic Functions
3
Topological charge
4 Vortex
Soliton in ferromagnets and winding number
5
Belavin-Polyakov Skyrmion
5.1 Scaling Theorem
5.2 O(3) Skyrmions
5.3 Skyrmions in Ferromagnets
5.4
Skyrmions in Easy-Axis Ferromagnets
5.5 Stabilization by the Dzyaloshinskii-Moriya interaction
5.6 Bimerons in Easy-Plane Ferromagnets
6 Spin
dynamics
6.1 Lagrangian
6.2 Landau-Lifshitz equation
6.3 Gilbert
damping and Landau-Lifshitz-Gilbert equation
6.4
Slonczewski spin transfer torque
6.5 Derivation of the Thiele equation from the LLG equation
6.6 Skyrmion Hall effects
6.7 Emergent electromagnetic field and topological Hall effects.
7 Quantum
spin liquid
7.1 Kitaev
spin liquid
7.2 Majumdhar-Ghosh model
7.3
Affleck-Kennedy-Lieb-Tasaki model
Quantum Physics 2016
1. DIRAC
THEORY
2.
SU-SCHRIEFFER-HEEGER MODEL
2.1
Jackiw-Rebbi solution
3. HONEYCOMB
DIRAC SYSTEM
3.1 Berry connection, Berry phase and Berry curvature
3.2 Hellmann-Feynman theorem
3.3
Thouless-Kohmoto-Nightingale-Nijs formula
3.4 Pontryagin number and Chern number
3.5 QHE in
the honeycomb system
3.6 Haldane
model and Kane-Mele model
4. MAJORANA
FERMION
4.1 Kitaev p-wave topological superconductor model
4.2 Z 2 topological invariant
4.3 Spinless p+ip-wave topological superconductor model
5. WEYL
SEMIMETAL
5.1 Monopole
charge
5.2 Weyl
semimetal, Chern number and anomalous Hall effects
5.3 Fermi arc
5.4 Weyl semimetal from Dirac semimetal with magnetic field
5.5
Adler-Bell Jackiew anomally
