PSI 2018/2019 - Quantum Information Review (Gottesman)

Motivations. Basic gates. Reversible computations.

Universal gates. No cloning theorem. Superdense coding. Density matrices.

CPTP maps POVMs. Measures of distance: fidelity and trace distance.

DiVincenzo's criteria. Ion traps. One qubit and two qubit gates. Cirac-Zoller gate.

Ion traps continued. Superconducting qubits. Jaynes-Cummings Hamiltonian. Other implementations.

Complexity. The halting problem. Church-Turing thesis. P and NP.

BQP. Classical and quantum oracles. Duetsch-Jozsa algorithm.

Factoring. RSA cryptography. Shor's algorithm.

Shor's algorithm continued. The quantum Fourier transform circuit.

Grover's algorithm.

Quantum error correcting codes. 3-qubit and 9-qubit codes.

Stabilizer codes. The threshold theorem of fault-tolerant quantum computing.