QIC 890 / CS 867 / CO 781:

Quantum Error Correction and Fault Tolerance, Winter 2022

Instructors:

Debbie Leung

Email: wcleung(at)uwaterloo(dot)ca

Michael Vasmer

Email: mvasmer(at)perimeterinstitute(dot)ca

Beni Yoshida

Email: byoshida(at)perimeterinstitute(dot)ca

TAs:

Elijah Durso-Sabina

Email: edursosabina(at)uwaterloo(dot)ca

Lane Gunderman

Email: lgunderman(at)uwaterloo(dot)ca

Lectures (Jan 05 - April 07):

Tue/Thur 11-12:15, QNC auditorium Mar 01-24 with recordings, student presentations April 05-07 live on zoom.

Office hours:

Instructors: after class or by appointment.

Slack channel (email Debbie for invitation)

Assessments:

7 assignments (total 70%)

Term project (30%)

Announcements:

Course materials

Resources:

  • Prerequisite: QIC 710
  • QECC notes from CO481 W2019
  • Textbook by Nielsen and Chuang
  • Daniel Gottesman's PhD thesis
  • Website for W2018 offering

    • Syllabus:

    Part 1 -- Quantum error correcting codes (Jan 6-27, 2022)

    Lecture 1: What is quantum noise?
  • Quantum operations and channels
  • Independence and low weight errors

    • Notes Recording

    Lecture 2: Basics of quantum error correction
  • The 9-bit Shor code
  • Discretization of quantum errors
  • Degenerate and non-degenerate codes
  • Quantum error correction criterion

    • Notes Recording 1 Recording 2 Recording 3 A1 (due Jan 21)

    Lecture 3-5: Stabilizer codes
  • Classical linear codes
  • Pauli group
  • Symplectic representation
  • Stabilizer codes
  • CSS codes
  • Erasure codes

    • Notes 1 Notes 2 Notes 3 Supp Recording 1 Recording 2 Recording 3 A2 (due Jan 31)

    Lecture 6-7: Evolution under the stabilizer framework
  • Clifford group
  • Group action on Pauli group
  • Encoded operations
  • Measurements
  • Gottesman-Knill Theorem
  • Gate teleportation
  • Ck hierachy

    • Notes 1 Notes 2 Recording 1 Recording 2 A3 (due Feb 09)

    Part 2 -- Fault-tolerance (Feb 1-17, 2022)

    Lecture 1: What is fault-tolerance?
  • Definition(s) of fault-tolerance
  • Standard "circuit noise" error model

    • Notes Recording

    Lecture 2: Fault-tolerant operations part I
  • Fault-tolerant error correction (Shor and Flag)
  • Fault-tolerant state preparation
  • Fault-tolerant measurements

    • Notes Recording A4 (Q1-2 due Feb 18, Q3 due Feb 25)

    Lecture 3: Fault-tolerant operations part II
  • Clifford group (recap)
  • Fault-tolerant gates
  • Transversal gates
  • Eastin-Knill theorem

    • Notes Recording

    Lecture 4: Fault-tolerant operations part III
  • 15 qubit Reed-Muller code
  • Logical gates via teleportation
  • Magic state distillation

    • Notes Recording

    Lecture 5: Threshold theorem part I
  • Formal fault-tolerance definitions
  • Local stochastic noise
  • Level reduction theorem

    • Notes Recording A5 (due Mar 04)

    Lecture 6: Threshold theorem part II
  • Concatenated codes
  • Proof of the threshold theorem
  • Assumptions of the threshold theorem

    • Notes Recording

    Part 3 -- Special topics (Mar 1-17, 2022)

    Lecture 1 (March 1, ~120 min):

  • Classical code
  • Toric code basic properties
  • Stability of ground states
  • Anyons

    • Notes for entire part 3 Recording

    Lecture 2 (March 3, ~120 min):

  • Anyons (continued)
  • Boundaries
  • Circuit complexity
  • SPT phases

    • Recording A6 (due Mar 18)

    Lecture 3 (March 17, ~120 min):

  • Toric code preparation circuit
  • Preparation with measurement
  • Color code

    • Recording

    Lecture 4 (March 22, ~90 min):

  • Cleaning lemma
  • Information storage bound

    • Recording

    Lecture 5 (March 24, ~90 min):

  • Clifford hierarchy
  • Bravyi-Koenig bound

    • Recording A7 (due Apr 08)

    Part 4 -- Student presentations (April 05 - 07, 2022)

    Note: scheduling and content are subject to minor changes

    Assessment materials

    Assignments:

    Problem sets are posted as part of the syllabus items. Please submit all assignments and term paper to Crowdmark.


    Term project topic suggestions: