This course will introduce key introductory concepts in quantum mechanics, quantum optics and quantum science. It is designed to provide a foundation for the more advanced courses in quantum science and technology offered at OIST. Topics will include: Wave particle duality, quantum interference, quantum states and their evolution, quantum cryptography, communication, computation and metrology. While sufficient mathematics knowledge is required to do well in the course, the focus is less on a rigorous mathematical approach than on covering a broad range of concepts and applications of quantum systems and technologies.
Topic 1: The Phenomena of Quantum Mechanics
- Particles and Waves
- Wave particle duality
- Quantum interference
Topic 2: Mathematical Prerequisites
- Linear Algebra
- Hermitian operators
- Projection operators and complete sets of states
- Unitary operators and Pauli matrices
- Traces of operators
- Density operators
Topic 3: Entanglement and Measurement
- Composite systems and partial traces
- Superposition and entanglement
- Measurement of quantum states
Topic 4: Quantum states and their characteristics
- Fock states
- Coherent states
- Squeezed states
o Application: Detecting gravitational waves
- Thermal states
Topic 5: Quantum states and their characteristics
- N00N states
- Distinguishing nonorthogonal quantum states
- Quantum state tomography
- Phase space distributions
Topic 6: Hamiltonians and Dynamics
- Simple Hamiltonians
- Quantum Dynamics
- Master equations
Topic 7: Quantum bits
- Quantum bits
- Entangled states
- EPR, Bell inequalities, and Local Realism
- Quantum information measures
Topic 8: Quantum cryptography
- Quantum non cloning
- Quantum random numbers generation
- Quantum key distribution
Topic 9: Advanced quantum communication
- Transmitting information with photons
- Quantum teleportation
- Quantum dense coding
- Quantum entanglement distribution
Topic 10: Quantum metrology
- Phase measurement: Heisenberg and Standard Quantum limits
- Quantum sensing
Topic 11: Quantum computation
- What is quantum computation?
- Quantum error correction
Topic 12: Quantum algorithms
- Deutch algorithm
- Search Algorithm
- Shor’s Algorithm
[*Topics covered will change depending on the class and their background]
Homework: 50%, Take home exam: 30%, Journal Club: 20%
Quantum Computation and Quantum Information, by M.A. Nielsen and I.L. Chuang (2010). Cambridge University Press
Introduction to Quantum Computing, by Ray LaPierre (2021). Springer Cham
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