Quantum Computation

Fall 2020

**Course description: **Topics
covered in Ph/CS 219A include density operators,
quantum operations, quantum entanglement, quantum circuits, and quantum
algorithms. Ph/CS 219B (Winter term, taught by
professor Kitaev) covers quantum error correction and
some special topics.

**Course
website**: Here

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

Teaching assistants:

Thom Bohdanowicz, email: thom(at)caltech(dot)edu

Charles Xu, email: cxu3(at)caltech(dot)edu

Office hours: Thursdays at 3 pm Pacific time. Use the Zoom link on Canvas to
join.

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.

**Piazza**:

We will use Piazza for class-related discussions. You will be automatically
added to our Piazza roster by clicking on the Piazza link in Canvas. In Piazza
you can post questions and comments about the course, and benefit from the
collective wisdom of your instructors and classmates. By default, your post
will be shared with the rest of the class, but you also have the option of
posting privately to the instructors, or of posting anonymously.

**Class meetings**:
*There are no synchronous lectures in this
class*. Lectures will be pre-recorded; videos can be streamed on our class Google
Drive. You can login to the Google Drive using your Caltech IMSS
credentials.

**Class materials**:
Lecture videos, slides, and other course materials will be posted on the Google
Drive. You can login to the Google Drive using your Caltech IMSS
credentials.

**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. If you have questions, you may post them on Piazza.

**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

**Update
(November 26):**

**The notes on quantum algorithms (Chapter
6) have been replaced by this new
version**. New sections have been added on: hidden subgroup problem,
quantum searching, quantum simulation, classical simulation of quantum
computation, and the local Hamiltonian problem.

**Update
(February 23, 2021):
Videos for all lectures have been posted on YouTube.**

**Course outline for fall term:
**Lecture 1:

Lecture 2: Density operators (slides)

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

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

Lecture 5: Qubit channels, master equation (slides)

Lecture 6: Bell inequalities, CHSH game (slides)

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

Lecture 8: Superdense coding and quantum teleportation (slides)

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

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

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

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

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

Lecture 14: Period finding (slides)

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

Lecture 16: Quantum searching (slides)

Lecture 17: Quantum simulation (slides)

Lecture 18: Local Hamiltonian problem (slides)

**Homework assignments:**

Charles will grade problem sets 1 and 4, Thom will grade problem sets 2 and 3.
Please contact the appropriate TA with questions pertaining to problem sets.

Problem
Set 1. States and measurements, due Friday 16 October.

Problem
Set 2. Quantum channels and entanglement, due Friday 30 October.

Problem
Set 3. Universal quantum gates, due Friday 20 November.

Problem
Set 4. Quantum algorithms, due Friday 4 December.