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):
Grading: • Problem Sets: 80% • Class Participation: 20%
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 1Solutions 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 April 25 Quantum Supremacy, PostBQP = PP stoquastic adiabatic computation and PostBPP. Slides 23 April 30 Quantum Supremacy, IQP Gate teleportation, random circuit sampling. Slides 24
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 1Solutions 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 April 25 Quantum Supremacy, PostBQP = PP stoquastic adiabatic computation and PostBPP. Slides 23 April 30 Quantum Supremacy, IQP Gate teleportation, random circuit sampling. Slides 24
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
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
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
April 25
Quantum Supremacy, PostBQP = PP stoquastic adiabatic computation and PostBPP.
Slides 23
April 30
Quantum Supremacy, IQP Gate teleportation, random circuit sampling.
Slides 24