A Course in Quantum Computation
This is a series of 19 videos which were lectures given as a bachelor degree level course at the Universitat Politècnica de Catalunya run by the Facultat de Matemàtiques in the spring term of 2021.
The content of the course is the following.
1. Introduction
2. Linear Algebra
3. Quantum Mechanics
4. Quantum Computation
5. Quantum Algorithms
6. Quantum Error-Correction
7. Quantum Information
The reference book used for the main part of the course is Quantum Computation and Quantum Information by Michael Nielsen and Isaac Chuang, which covers most of the course and a secondary reference is the book by Phillip Kaye, Raymond Laflamme and Michele Mosca, Introduction to Quantum Computing. There are some parts which are original and novel but hopefully these are well explained in the videos.
Class 1
1.1 The double-slit experiment and Wheeler's interferometer
1.2 Quantum bits
1.3 Multiple qubits
1.4 Quantum computation
Class 2
1.5 Quantum teleportation
1.6 Quantum algorithms
1.7 Complexity classes
Class 3
2.1 Dirac notation
2.2 Linear operators and diagonalisation
Class 4
2.3 Tensor products
2.4 Traces of endomorphisms
2.5 Polar and singular value decomposition
2.6 Density operators
Class 5
2.7 Schmidt decomposition
3.1 State space
3.2 Evolution of closed quantum systems
Class 6
3.3 Measurement of a quantum system
3.4 Projective measurements
3.5 Composite systems
Class 7
3.6 Partial trace
3.7 Purification
3.8 Bell inequality
3.9 Heisenberg uncertainty principle
Class 8
4.1 Controlled operations
4.2 Universal quantum gates
Class 9
4.2 Universal quantum gates
4.3 Measurements
4.4 A discrete set of quantum gates
Class 10
4.5 Approximating quantum circuits
4.6 Quantum computational complexity
Class 11
5.1 Quantum Fourier transform
5.2 Phase estimation
Class 12
5.2 Phase estimation (order-finding, quantum factorisation, discrete log)
5.3 Grover's algorithm
Class 13
5.4. Optimality of the search algorithm
5.5. BB84 protocol
6.1. Quantum operations
Class 14
6.2: Quantum error-correction
6.3: Stabiliser codes
Class 15
6.4. Stabiliser codes as binary codes
6.5. Fault tolerant quantum computation
Class 16
7.1. Shannon entropy
7.2. Relative entropy
7.3. Conditional entropy
7.4. Von Neumann entropy
Class 17
7.4. Von Neumann entropy
7.5. Von Neumann entropy for composite systems
7.6. Measurement and entropy
7.7. Entropy of a mixture of quantum states
Class 18
7.8. Holevo bound
7.9. Quantum Singleton bound
Class 19
7.10. Entanglement measures
7.11. Quantum supremacy
Updated 24 August 2021