Quantum Computation

Fall 2021

**Course description: **Ph/CS 219A is the first term in a three-term course on
quantum computation and quantum information science. Topics covered in 219A include
density operators, quantum operations, quantum entanglement, quantum circuits,
and quantum algorithms. Topics to be covered in Ph/CS
219B and 219C include quantum error correction, fault-tolerant quantum
computing, quantum Shannon theory, and some special topics.

**Course
website**: Here

**Instructor:
**John Preskill,
206 Annenberg, X-6691, email: preskill(at)caltech(dot)edu

Teaching assistants:

Kyle Gulshen, email: kgulshen(at)caltech(dot)edu

Tian Wang, email: twang3(at)caltech(dot)edu

Office hours: To be announced.

Students may also request meetings with TAs at other times.

**Canvas:**

We will be using the Canvas Learning Management System. You can login to Canvas
using your Caltech IMSS credentials.

**Class meetings**:
Monday and Wednesday 2:30 – 3:55 pm in East Bridge 201 (Feynman Lecture Hall),
starting on September 27. Lectures will be recorded using the Echo360 system in
the lecture hall. Video files will be available in Canvas at the Echo360 link.

**Homework
assignments and grading**: The course is graded pass-fail. Homework
will be submitted, and graded homework will be returned, using Canvas.

You may receive partial credit if you describe a thoughtful approach to the problem, even if you are unable to solve it completely.

**Lectures and references:
**The primary reference for most of the lectures will be these lecture
notes (JP). Other useful books are

Other recommended lecture notes: John Watrous, Umesh Vazirani, Andrew Childs, Scott Aaronson, Ronald de Wolf

**Material from Fall 2020:
**

**Here are slides from last fall. This
year’s material will be broadly similar, but we expect to devote more time to
quantum algorithms. **

Lecture 1 (2020):** **Introduction (slides)

Lecture 2 (2020): Density operators (slides)

Lecture 3 (2020): Convexity, HJW theorem, generalized measurements (slides)

Lecture 4 (2020): Quantum channels, complete positivity, channel state duality
(slides)

Lecture 5 (2020): Qubit channels, master equation (slides)

Lecture 6 (2020): Bell inequalities, CHSH game (slides)

Lecture 7 (2020): Bell polytope and its dual, quantum vs classical models (slides)

Lecture 8 (2020): Superdense coding and quantum
teleportation (slides)

Lecture 9 (2020): Circuit complexity, P and NP, NP-completeness (slides)

Lecture 10 (2020): BPP and MA, Reversible computing, BQP and QMA (slides)

Lecture 11 (2020): Quantum circuits, universal gates. (slides)

Lecture 12 (2020): Universal gates continued, Solovay-Kitaev
theorem (slides)

Lecture 13 (2020): Black Box model, Deutsch-Jozsa
problem, Simon’s problem (slides)

Lecture 14 (2020): Period finding (slides)

Lecture 15 (2020): Factoring, public key cryptography, phase estimation (slides)

Lecture 16 (2020): Quantum searching (slides)

Lecture 17 (2020): Quantum simulation (slides)

Lecture 18 (2020): Local Hamiltonian problem (slides)

**Homework assignments:**

Problem
Set 1. States and measurements, due Friday 15 October.

Problem
Set 2. Channels and entanglement, due Friday 29 October.

Problem
Set 3. Universal gates, due Friday 12 November.

Problem
Set 4. Quantum algorithms, due Friday 3 December