Date |
Topic |
Notes |
Jan. 22 |
Mathematical Models in Theoretical Physics, Classical Probability Theory and Linear Algebra |
Slides 1 |
Jan. 24 |
Generalized Probability Theory, Axioms of Quantum Mechanics |
Slides 2 |
Jan. 29 |
Physical Content and Hamiltonians, Qubits: Observables and Operations |
Slides 3 |
Jan. 31 |
Amplitudes vs Mixtures, Incompatible Measurements, Introduction to Entanglement |
Slides 4 |
Feb. 5 |
Entangling Hamiltonians, Quantum subsystems density matrices, partial trace, Schmidt decomposition |
Slides 5 |
Feb. 7 |
Quantum Channels: Kraus operator-sum representation, depolarizing, dephasing, amplitude-dampening channels |
Slides 6 |
Feb. 14 |
Classical Information Theory Shannon entropy, relative entropy, mutual information
Shannon's paper , Witten's notes |
Slides 7 |
Feb. 19 |
Homework 1: entanglement and correlations, distance between quantum states, quantum channels, capacity and mutual information. Due Date: March 7th, 2019. |
Problem Set 1 Solutions |
Feb. 21 |
Convex functions, Data Processing Inequalities, Pinsker's Inequality and Correlation Functions
| Slides 8 |
Feb. 26 |
von Neumann entropy, quantum entropy inequalities, The quantum no-cloning theorem
| Slides 9 |
Feb. 28 |
Quantum teleportation, partial information, negative quantum conditional entropy
| Slides 10 |
Mar. 5 |
EPR thought experiment, Bell's inequality
| Slides 11 |
Mar. 7 |
Randomness certification, RSA encryption, Quantum Key Distribution, Quantum Money
| Slides 12 |
Mar. 19 |
Compression over noiseless channels, theorems of Shannon, Schumacher, Holevo
| Slides 13 |
Mar. 21 |
Entanglement cost, distillable entanglement, entanglement monogamy, black hole firewalls
| Slides 14 |
Mar. 22 |
Homework 2: Quantum Key Distribution, Quantum Money, Noisy Teleportation, Nonlocal Games. Due Date: April 4th, 2019. |
Problem Set 2 |
Mar. 26 |
Constraint satisfaction problems, Local Hamiltonians.
| Slides 15 |
Mar. 28 |
Simulating quantum dynamics, Quantum Phase Estimation
| Slides 16 |
April 2 |
Classical complexity theory P, NP, co-NP, MA, AM, PH, PP, PSPACE
| Slides 17 |
April 4 |
Quantum complexity theory BQP, QMA, Feynman-Kitaev history states
Quantum NP - A Survey
| Slides 18 |
April 9 |
Homework 3: Local Hamiltonians and NP-completeness, Circuit verifiers, non-destructive measurements, Phase estimation. Due Date: April 18th, 2019. |
Problem Set 3 |
April 9 |
The local Hamiltonian problem is QMA-complete
| Slides 19 |
April 11 |
Guest lecture: Rafael Alexander Tensor Network States, MPS, PEPS, MERA
| Slides |
April 16 |
The quantum marginal consistency problem is QMA-complete. Liu's paper.
| Slides 20 |
April 18 |
Homework 4: Marginal consistency, history state Hamiltonians, matrix product states. Due: April 30th, 2019. |
Problem Set 4 |
April 18 |
Path integrals and complexity BQP, QMA in PP.
| Slides 21 |
April 23 |
Path integrals and complexity Stoquastic LH in AM, quantum Monte Carlo.
| Slides 22 |