CS 294: Quantum Learning Theory

General Information

Assignments

Homework 1, due Tuesday September 24, 11:59pm

Homework 2, due Tuesday October 15, 11:59pm

Homework 3, due Monday November 4, 11:59pm

Homework 4, due Friday December 6, 11:59pm

Lectures

• Lecture 1 (Aug 28): Course overview and discriminating two pure states (scribe notes)

• Lecture 2 (Sep 4): Review of quantum measurements and discriminating mixed states (scribe notes)

• Lecture 3 (Sep 9): Average case discrimination of two mixed states (scribe notes)

• Lecture 4 (Sep 11): Worst case discrimination of two mixed states (scribe notes)

• Lecture 5 (Sep 18): Quantum fidelity (scribe notes)

• Lecture 6 (Sep 23): The Pretty Good Measurement (scribe notes)

• Lecture 7 (Sep 25): The swap test, part 1 (scribe notes)

• Lecture 8 (Sep 30): The swap test, part 2 (scribe notes)

• Lecture 9 (Oct 2): Intro to quantum tomography (scribe notes)

• Lecture 10 (Oct 7): The "textbook" tomography algorithm (scribe notes)

• Lecture 11 (Oct 9): The symmetric subspace, part 1 (scribe notes)

• Lecture 12 (Oct 14): The symmetric subspace, part 2, and optimal pure state tomography (scribe notes)

• Lecture 13 (Oct 16): Optimal unentangled tomography (scribe notes)

• Lecture 14 (Oct 21): Efficient unentangled tomography and learning with high probability

• Lecture 15 (Oct 23): Introduction to shadow tomography (scribe notes)

• Lecture 16 (Oct 28): Introduction to shadow tomography, part 2 (scribe notes)

• Lecture 17 (Oct 30): Introduction to shadow tomography, part 3, and quantum state certification

• Lecture 18 (Nov 4): Quantum state certification, part 2

• Lecture 19 (Nov 6): Introduction to representation theory (scribe notes)

• Lecture 20 (Nov 13): The regular representation and irreps of the symmetric group (scribe notes)

• Lecture 21 (Nov 18): Irreps of the unitary group and Schur-Weyl duality (scribe notes)

• Lecture 22 (Nov 20): Spectrum estimation via representation theory (scribe notes)

• Lecture 23 (Nov 25): Full state tomography via representation theory

• Lecture 24 (Dec 2): Shadow tomography, part 1 (scribe notes)

• Lecture 24 (Dec 4): Shadow tomography, part 2 (scribe notes)

List of topics

• Quantum state discrimination
  Two state distinguishing
  Pretty good measurement
• Quantum state learning and testing
  Purity testing
  Spectrum estimation
  Quantum tomography
  Quantum state certification
• Mathematics of quantum state tomography
  Haar random unitaries and vectors
  The symmetric subspace
  Representation theory of the symmetric and general linear groups
• Shadow tomography
  Classical shadows
  Shadow tomography
• Learning and testing structured states
  Testing product states
  Pseudorandom states
  Learning local Hamiltonians
  Learning short-depth quantum states

Prerequisites

Evaluation