Quantum Error Correction and Fault Tolerance, Winter 2024
Debbie Leung
Email: wcleung(at)uwaterloo(dot)ca
Michael Vasmer
Email: mvasmer(at)perimeterinstitute(dot)ca
Kohdai Kuroiwa
Email: kkuroiwa(at)uwaterloo(dot)ca
Thur 10:00-12:50, QNC 1201
10 lectures in Jan 11 - Mar 21
Term project presentations Apr 01-05, to be held at this zoom link
Instructors: after class or by appointment
TA office hour: dynamically decided
Piazza: (Sign up here or email Debbie for invitation)
5 assignments (total 75%)
Term project (25%)
Posted Apr 01, 2024, 02:30
Presentations are held on zoom, the link has been emailed to you at the address from LEARN, shared above, and on piazza.
Posted Mar 13, 2024, 11:30
A4, A5, recordings for lectures 7, 8 uploaded. As access to this website will be more limited March 17 - 26, please watch out for recordings on the playlist, and revisions of A4 or notes on piazza.
Posted Mar 05, 2024, 11:15
Notes 2 for lecture 7 and revised A3 posted (those were already shared on piazza). Notes for lectures 8-10 posted.
Posted Feb 23, 2024, 20:30
Notes 1 for lecture 7, and A3 posted. You can start on A3 with the help of the notes.
Posted Feb 16, 2024, 20:10
Recording for lecture 6 posted, and notes on Bacon-Shor code add.
Posted Feb 14, 2024, 19:10
Notes for lecture 6 posted.
Posted Feb 8, 2024, 22:50
Reccording for lecture 5 posted, and there is now a full playlist just under the link for livestreaming.Lecture 11 is cancelled to make time for the 10-12 hours of term project presentations, which will be online, and spread out over several days. We will group the presentations according to topics, and strongly encourage attendance on materials of your interest that we do not have time to cover in the regular lectures. We will coordinate students with related interests. Selection of topics will start in reading week.
Posted Feb 8, 2024, 14:30
Second set of notes for today's lecture posted.
Posted Feb 6, 2024, 01:50
A2 posted (near lecture 4). You can work on Q1 and Q2 already.Recording for lecture 4 posted.
We will keep livestreaming through lecture 10!
Posted Jan 31, 2024, 16:20
Notes for lectures 4-5 and recording for lecture 3 posted.Still discussing if we have livestreaming tomorrow due to freezing drizzle forecast overnight.
Posted Jan 24, 2024, 19:50
Notes for lecture 2 p10 onwards revised and under "Notes 2" (file ending with part2.pdf)Link to livestreaming moved to "Lectures" section close to top of this website.
Posted Jan 23, 2024, 02:00
Assignment 1 is posted (under Lectures 2-3).You should receive an invitation to submit solutions from Crowdmark.
Also, recordings are now available on youtube!
Posted Jan 17, 2024, 22:00
Supp notes for lecture 1 and notes for lecture 2 uploaded. The same link for live-streaming for lecture 1 works for lecture 2. Assignment 1 will be posted end of the week.
Posted Jan 10, 2024, 18:45
Live-streaming on MS Teams will be available (see link with lecture 1 description) and recording will be provided by end of the week.
Posted Jan 10, 2024, 18:40
Notes (2 sets) for lecture 1 uploaded.
Posted Dec 09, 2023, 13:15
Website was set up.
Course description:
Students will learn:(1) Principles for quantum error correction
(2) Stabilizer formalism
(3) Important classes of quantum error correcting codes(4) Fault-tolerant quantum computation and the threshold theorem
(5) Select applications of QECC
Course materials
Prerequisite: QIC 710 QECC notes from CO481 W2019 Textbook by Nielsen and Chuang Daniel Gottesman's PhD thesis John Preskill Lecture notes for Physics 229 Website for W2018 offering Website for W2022 offering
Lectures 1-2: Basics of quantum noise and quantum error correctionLectures 2-3: Stabilizer codesQuantum operations and channels Independence and low weight errors The 9-bit Shor code Discretization of quantum errors Quantum error correction criterion Degenerate and non-degenerate codes Classical linear codes Pauli group Symplectic representation Stabilizer codes CSS codes Erasure codes Lecture 3 recording (missing last 30 mins on Notes 3, on erasures)
A1, due Feb 02, 7pm on Crowdmark
Lecture 4: Evolution under the stabilizer frameworkClifford group Group action on Pauli group Encoded operations Measurements Gottesman-Knill Theorem Gate teleportation Ck hierachy Lecture 4 recording (covering Notes 1, missing p3-8)
Covered in lecture 6: Notes 2 Bacon-Shor-code example References
A2, due Feb 23, 7pm on Crowdmark
Lecture 5: Quantum LDPC codes (I)
Lecture 6: Toric codeLinear codes revisited - Tanner graph representation Classical low-density parity-check (LDPC) codes Hypergraph product codes Properties of hypergraph product codes (stabilizer weight) Toric code as a hypergraph product of two classical repetition codes Lecture 7: Quantum LDPC codes (II)Definition as stabilizer code in lattice picture Code parameters Syndromes as excitations Decoding algorithms Distance vs other measures of error correction capability Connections to physics and fault-tolerant quantum computation Properties of hypergraph product codes (number of logical qubits and code distance) Classical expander codes Quantum expander codes via the hypergraph product A3 (revised), due Mar 08, 7pm on Crowdmark
Lecture 8: What is fault-tolerance and fault-tolerant operations (I)Definition(s) of fault-tolerance Standard "circuit noise" error model Fault-tolerant error correction (Shor and Flag) Fault-tolerant state preparation Fault-tolerant measurements Lecture 9: Fault-tolerant operations (II)
Clifford group (recap) Fault-tolerant gates Transversal gates Eastin-Knill theorem 15 qubit Reed-Muller code Logical gates via teleportation Magic state distillation A4, due Mar 22, 7pm on Crowdmark
Lecture 10: Threshold theorem
Formal fault-tolerance definitions Local stochastic noise Level reduction theorem Concatenated codes Proof of the threshold theorem Assumptions of the threshold theorem A5, due April 12, 7pm on Crowdmark
Term project areas (additional applications of QECC):
fault-tolerance with the toric code, anyons and topological quantum computation QECC and topological phases, and other applications of QECC to many body physics single-shot error correction flag fault-tolerant quantum error correction and computation applications of QECC to quantum cryptography (nonlocal games, quantum key distillation, self-testing, secret sharing) quantum error correction and entanglement purification the HaPPY code: toy models for the AdS/CFT bulk/boundary correspondence
Note: scheduling and content are subject to minor changes