Quantum Computation

Spring 2004

**Go to home page for
Ph219/CS219 in past years.**

**Go to home page for
Ph219/CS219 earlier this year.**

**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

**Instructor:
**John Preskill
, 448 Lauritsen, X-6691, email: preskill@theory.caltech.edu

Teaching assistants:

Ben Toner, 449 Lauritsen, X-6595 email: toner@caltech.edu

**Lectures and references:**

**Part**** ****I.**** Quantum error correction**

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
computation**

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).

That’s all!

**Homework assignments:**

Problem Set 1 [PS] [PDF]
(posted

Solution Set 1 [PS] [PDF]