Course description: The course covers these topics: (1) Quantum error-correcting codes, (2) Fault-tolerant quantum computing, (3) Quantum computation with nonabelian anyons. Initially, I had also hoped to cover (4) Security of quantum key distribution (e.g., the BB84 and B92 protocols), and (5) Security of other quantum protocols (e.g, coin flipping, digital signatures, and secure computation). But there wasn’t enough time.
Class meetings: Tuesdays and Thursdays in 269 Lauritsen.
Lectures and references:
The reference for the first couple of weeks is Chapter 7 of my lecture notes (“Quantum error correction”).
Lecture 1 (3/30): Criterion for error correction, distance of a code, fidelity of error recovery.
Lecture 2 (4/1): CSS codes, 7-qubit code, stabilizer codes.
Lecture 3 (4/6): Stabilizer codes continued. 5-qubit code.
Lecture 4 (4/8): Measuring check operators, encoding, quantum Gilbert-Varshamov bound.
Lecture 5 (4/13): Quantum Singleton bound, quantum Reed-Muller codes, concatenated codes.
Lecture 6 (4/15): Toric codes (quant-ph/0110143).
Part II. Fault-tolerant quantum
Lecture 7 (4/20) : Fault-tolerant quantum error correction (quant-ph/9712048).
Lecture 8 (4/22) : Fault-tolerant Clifford group gates (quant-ph/9807006, quant-ph/9802007).
Lecture 9 (4/27) : Fault-tolerant C_3 gates (quant-ph/0002039).
Lecture 10 (4/29): Fault tolerance with polynomial codes (quant-ph/9906129); distillation of quantum software (quant-ph/0403025).
Lecture 11 (5/4) : Accuracy threshold for quantum computation (quant-ph/9906129, quant-ph/9702058).
Lecture 12 (5/6) : Quantum fingerprints (quant-ph/0102001), lecture by Ben Toner.
Lecture 13 (5/11): Accuracy threshold continued.
Part III. Topological quantum computation
The primary reference for my lectures on anyons will be these lecture notes: [PS (2.2 MB)] [PDF (0.4 MB)] (updated
Note: some printers may choke on the .ps file because of its large size. If you have trouble, try the .pdf file.
Lecture 14 (5/13): Spin and statistics in two spatial dimensions.
Lecture 15 (5/18): Braid group, topological degeneracy, nonabelian Aharonov-Bohm effect.
Lecture 16 (5/20): The nonabelian superconductor model.
Lecture 17 (5/25): Quantum computing with fluxons (quant-ph/0206128).
Lecture 18 (5/27): CANCELLED!!
Lecture 18 (6/1): Simulating a topological quantum computer with a quantum circuit (quant-ph/0001071).
Lecture 19 (6/3): Simulating a quantum circuit with a topological quantum computer (quant-ph/0001108).