Quantum Error Correction and Fault Tolerance, Winter 2022

Debbie Leung

Email: wcleung(at)uwaterloo(dot)ca

Michael Vasmer

Email: mvasmer(at)perimeterinstitute(dot)ca

Beni Yoshida

Email: byoshida(at)perimeterinstitute(dot)ca

Elijah Durso-Sabina

Email: edursosabina(at)uwaterloo(dot)ca

Lane Gunderman

Email: lgunderman(at)uwaterloo(dot)ca

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

Instructors: after class or by appointment.

Slack channel (email Debbie for invitation)

7 assignments (total 70%)

Term project (30%)

Posted Jan 19, 2022, 23:59

A2 posted, Notes 2 for stabilizer codes replaced (for typos), supplementary notes for stabilizer codes and first few pages for Clifford group added.

Posted Jan 18, 2022, 23:00

Recording for Jan 18 lecture posted.

Posted Jan 15, 2022, 00:30

For A1 Q2b and Q3, you can consider a pure state encoded input and analyse what is the corresponding output. In both cases, decode into an unecnoded qubit state.

Posted Jan 13, 2022, 23:30

Notes 1 for Lectures 3 & 4 reposted (pages reordered), recordings for Jan 13 lecture posted (in 3 separate videos).

Posted Jan 12, 2022, 23:45

Removed "where c_{ij} is the (i,j)-entry of a positive semidefinite matrix C" in the QECC condition; A1Q1 revised accordingly.

Posted Jan 11, 2022, 23:45

A1 revised. Crowdmark submission invitations sent.

Posted Jan 11, 2022, 18:00

Recording for lecture 2, A1 (tentative), and notes for lectures 3-4 uploaded; Crowdmark submission invitations will be sent shortly.

Posted Jan 06, 2022, 16:00

Recording for lecture 1 uploaded, slack channel created

Posted Jan 04, 2022, 23:30

Notes for lectures 1 & 2 uploaded.

Posted Dec 21, 2021, 14:30

Website was set up.

Course materials

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

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

Lecture 1: What is quantum noise?Lecture 2: Basics of quantum error correctionQuantum operations and channels Independence and low weight errors 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 codesClassical 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 frameworkLecture 7: Measurement induced dynamicsClifford group Group action on Pauli group Ck hierachy Encoded operations Measurements Gottesman-Knill Theorem Lecture ?: Bounds on quantum error correctionGate teleportation MBQC as repeated teleportation Quantum Hamming bound Quantum Gilbert-Varshamov bound Quantum Singleton bound

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

Lecture 1: What is fault-tolerance?Lecture 2: Fault-tolerant operations part IDefinition of fault-tolerance Standard "circuit noise" error model Fault-tolerant error correction (Shor and Flag) Lecture 3: Fault-tolerant operations part IIFault-tolerant error correction through repetition of stabilizer measurements Fault-tolerant state preparation Fault-tolerant measurements Lecture 4: The threshold theoremClifford group (recap) Fault-tolerant gates Transversal gates Eastin-Knill theorem Magic state distillation (15 qubit Reed-Muller code) Lecture 5: Threshold theorem assumptionsConcatenated codes Threshold theorem Lecture 6: Fault-tolerant measurement-based quantum computingAssumptions of the threshold theorem re-examined Gate assumptions Error model assumptions 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