Quantum Computer Science

Synopsis

1. Historical and physical context
1.1 The birth of quantum mechanics
1.2 The status of quantum mechanics
1.3 The birth of quantum informatics
1.4 The status of quantum informatics
2 Qubits vs. bits
2.1 Acting on qubits
2.2 Describing a qubit with complex numbers
2.3 Describing two qubits
3 von Neumanns pure state formalism
3.1 Hilbert space
3.2 Matrices
3.3 Tensor structure
3.4 Dirac notation
4 Protocols from entanglement
4.1 Bell-base and Bell-matrices
4.2 Teleportation and entanglement swapping
5 The structure of entanglement
5.1 Map-state duality and compositionality
5.2 The logic of bipartite entanglement
5.3 Quantifying entanglement
5.4 Trace
6 Algorithms and gates
6.1 Special gates
6.2 The Deutch-Jozsa algorithm
6.3 Grover's algorithm
6.4 Shor's factoring algorithm
6.4.1 Period finding
6.4.2 Factoring and code-breaking
6.5 Quantum key distribution
7 Mixed states
8 Quantum logic and Gleason's theorem
9 Mixed operations
10 More on tensors
11 Graphical language for quantum informatics
11.1 Symmetric monoidal categories
11.2 dagger-compact categories