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 05):

Tue/Thur 11-12:15, live on zoom (until further notice)

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 & 4: 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 A2 (due Jan 28)

    Lecture 5 & 6: Evolution under the stabilizer framework
  • Clifford group
  • Group action on Pauli group
  • Ck hierachy
  • Encoded operations
  • Measurements
  • Gottesman-Knill Theorem
  • Notes 1 A3 (due Feb 03)

    Lecture 7: Measurement induced dynamics
  • Gate teleportation
  • MBQC as repeated teleportation
  • Lecture ?: Bounds on quantum error correction
  • Quantum Hamming bound
  • Quantum Gilbert-Varshamov bound
  • Quantum Singleton bound
  • Part 2 -- Fault-tolerance (Feb 1-17, 2022)

    Lecture 1: What is fault-tolerance?
  • Definition of fault-tolerance
  • Standard "circuit noise" error model
  • Fault-tolerant error correction (Shor and Flag)
  • Lecture 2: Fault-tolerant operations part I
  • Fault-tolerant error correction through repetition of stabilizer measurements
  • Fault-tolerant state preparation
  • Fault-tolerant measurements
  • Lecture 3: Fault-tolerant operations part II
  • Clifford group (recap)
  • Fault-tolerant gates
  • Transversal gates
  • Eastin-Knill theorem
  • Magic state distillation (15 qubit Reed-Muller code)
  • Lecture 4: The threshold theorem
  • Concatenated codes
  • Threshold theorem
  • Lecture 5: Threshold theorem assumptions
  • Assumptions of the threshold theorem re-examined
  • Gate assumptions
  • Error model assumptions
  • Lecture 6: Fault-tolerant measurement-based quantum computing
  • One-way quantum computer
  • Raussendorf model
  • Part 3 -- Special topics (Mar 1-17, 2022)

    Lectures 1-2: Toric code

    Lectures 3-4: Topological phases and color codes

    Lectures 5-6: Decoupling and scrambling

    Part 4 -- To be determined (Mar 22 - Apr 5, 2022)

    Student presentations, make-up classes, guest lecture, additional special topics

    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.