Physics 572 Spring 2019

Quantum Information Theory

 

Instructor: Prof. Elizabeth Crosson

Office: Physics and Astronomy Room 13

Email: crosson@unm.edu

Office Hours: Tuesday 2:00-3:00, Wednesday 11:00-12:00, room 13

Lectures: Tuesday and Thursday 11:00-12:15, Physics and Astronomy room 5

Online Texts (Optional):

“Lectures notes on Quantum Information and Computation” J. Preskill
“From Classical to Quantum Shannon Theory”, M. Wilde
“Quantum Information Meets Quantum Matter”, B. Zeng, X. Chen, D.L. Zhou, X.G. Wen

Grading:
• Problem Sets: 80%
• Class Participation: 20%

PDF Syllabus

Schedule of Topics


Part 1: Quantum Information Processing
Axiomatic Quantum Mechanics
Probability and Statistics
Mixed States and Quantum Operations
Classical Information Theory
Entanglement Measures and Local Operations
Bell’s Inequality and Hidden Variable Theories
Quantum Communication and Cryptography


Part 2: Quantum Physics and Complexity
Quantum Many-Body Physics
Local Hamiltonians and Quantum Computation
Phases of Quantum Matter
Entanglement in Quantum Ground States
Classical and Quantum Computational Complexity
The Local Hamiltonian Problem
Classical Simulations of Quantum Systems
Sampling Complexity and Quantum Supremacy

Lecture Notes


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