C191: Syllabus
1. Basic QM (4 lectures)
F Aug 29 Axioms
States, Hamiltonians, observables Hilbert space, tensor product, partial trace
W Sep 3 Qubits, multiple qubits, Bloch sphere
Physical qubits
F Sep 5 Bra-ket notation, density matrices
W Sep 10 Evolution, unitary maps, positive maps, representation frames (Heisenberg, Schrodinger, interaction, rotating)
2. Circuit model QC (3 lectures)
F Sep 12 Reversible computation
Circuits, elementary one- and two-qubit gates
W Sep 17 Measurements, principle of deferred measurement
Teleportation
F Sep 19 Universality
Circuit simulation, Solvay-Kitaev, Clifford group
3. CS complexity (1 lecture)
W Sep 24 Complexity classes, interpretation and motivation
BQP and its relation to BPP, P and NP
Oracle model
Hamiltonian complexity
4. Quantum classical separations (1 lecture)
F Sep 26 No-cloning, uncertainty principle, superdense coding
Deutsch-Josza algorithm
5. Foundations and Interpretations, entanglement (1 lecture)
W Oct 1 The notion of state
Classical formal mechanics
Notion of phase space distributions
Wave function as state (maximal knowledge and uncertainty)
Wave function as distribution (non-positivity)
Interpretations: Copenhagen/operational, many-worlds, Bayesian,
EPR, Bell's theorem
6. QKD, Cryptography (2 lectures)
F Oct 3 Classical cryptographic models (public, private)
Notions of security
Fundamental arguments for why quantum is more secure
W Oct 8 QKD protocols (BB84, GG02)
Postprocessing details, error correction, privacy amplification
7. Measures on state space, distinguishability (1 lecture)
F Oct 10 POVMs
Notions of distinguishability (mathematical, operational), distance measures for classical and quantum distributions
State and process fidelity, diamond norm
8. Open quantum systems, decoherence, error
correction, fault tolerance (5 lectures)
W Oct 15 Open systems, notion of decoherence and dephasing
Hamiltonian formulation, partial trace, master equations
F Oct 17 Kraus maps
Common error models for QC
W Oct 22 Classical and quantum error correction codes
F Oct 24 Implementing ECC and fault tolerance theorem
W Oct 29 Error avoidance: decoherence free subspaces/subsystems
9. Algorithms (4 lectures)
F Oct 31 Grover
W Nov 5 QFT
F Nov 7 Phase estimation
W Nov 12 Period finding, Shor, factoring
10. Implementations (2 lectures)
F Nov 14 Superconducting circuits (Prof. Irfan Siddiqi)
W Nov 19 Ion traps (Prof. Hartmut Haffner)
11. Entanglement (1 lecture)
F Nov 21 Notion of entanglement, EPR, Bell
Entanglement in bipartite pure states, measures
Multipartite pure state entanglement, measure
Mixed state entanglement, measures
Bound entanglement and discord
12. Alternate QC models (1 lecture)
W Nov 26 Quantum simulation, analog and digital
Adiabatic QC
F Nov
28 Thanksgiving
holiday
13. Student Presentations (2 lectures)
W Dec 3
F Dec 5