Quantum Computing Course Outline
Introduction to Quantum Computing
- Quantum Mechanics
- Qubits and Quantum Memory
- Elementary Gates
Overview of Circuit Model and Deutsch-Jozsa
Introduction to Simon’s Algorithm
The Fourier Transform
- Classical Discrete Fourier Transform
- Fast Fourier Transform
- Application – Multiplying Two Polynomials
- Quantum Fourier Transform
- Quantum Circuit
Shor’s Factoring Algorithm
Hidden Subgroup Problem
Grover’s Search and Quantum Walk Algorithm
- Grover’s Algorithm
- Amplitude Amplification
- Application: Satisfiability
- Quantum Walk
- Applications
Overview of Hamiltonian Simulation
Introduction to HHL Algorithm
- Linear Systems Problem
- HHL Algorithm for Linear Systems
- Improving HHL Algorithm Complexity
Quantum Query Lower Bounds
Quantum Complexity Theory
Quantum Encodings with a Non-Quantum Application
Quantum Communication Complexity
Entanglement and Non-Locality
- Quantum Non-Locality
- CHSH: Clauser-Horne-Shimony-Holt
- Magic Square Game
Introduction to Quantum Cryptography
Error-Correction and Fault-Tolerance
- Introduction
- Classical Error-Correction
- Quantum Errors
- Quantum Error-Correcting Codes
- Fault-Tolerant Quantum Computation
- Concatenated Codes and Threshold Theorem