How quantum computing works

From classical bits to qubits: state vectors and Dirac notation, measurement, compound systems, quantum circuits, and entanglement, with teleportation, superdense coding and the CHSH game.

1. 01 Classical information
2. 02 Quantum information
3. 03 Multiple systems: classical
4. 04 Multiple systems: quantum
5. 05 Quantum circuits
6. 06 Quantum states and measurements
7. 07 Limitations of quantum measurements
8. 08 Entanglement

What a quantum computer does better: query problems from Deutsch to Simon, the cost of classical arithmetic, phase estimation and Shor's factoring, and Grover's search.

1. 09 Query-model algorithms
2. 10 The cost of classical algorithms
3. 11 Classical circuits as quantum circuits
4. 12 Phase estimation and factoring
5. 13 Grover's algorithm

Density matrices for mixed states, quantum channels and their representations, general measurements, purifications and fidelity.

1. 14 Density matrices
2. 15 Quantum channels
3. 16 Channel representations
4. 17 General measurements
5. 18 State discrimination and tomography
6. 19 Purifications
7. 20 Fidelity

How a noisy quantum computer can still compute: error-correcting codes, stabilizers, CSS, toric, surface and color codes, and fault tolerance up to the threshold theorem.

1. 21 Quantum error correction
2. 22 The stabilizer formalism
3. 23 Quantum code constructions
4. 24 Fault-tolerant quantum computing