Ph219/CS219
Quantum Computation
Spring 2026

Course description: Ph/CS 219C is the third term in a three-term course on quantum computation and quantum information science. Topics covered in 219A included density operators, quantum operations, quantum entanglement, quantum circuits, and quantum algorithms. Ph/CS 219B covered quantum error correction and fault-tolerant quantum computing.

Ph/CS 219C will build on 219B by covering additional topics related to error correction and fault tolerance as well as other topics to be decided. But the course should be accessible to students who did not take 219B.

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

Teaching assistants: 
Kyle Gulshen, email: kgulshen(at)caltech(dot)edu
Preksha Naik, email: pnaik(at)caltech(dot)edu
TA Office hours: Tuesdays on weeks where problem sets are due. Tuesday 2-3pm in Downs 107. Please also feel free to email TAs any time to request additional office hours. 

Class meetings:
Monday and Wednesday 2:30 – 3:55 pm in 269 Lauritsen, starting March 30. The lectures are in-person only and will not be recorded. 
There will be no lecture on May 6.

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.

References:
The primary reference for most of the lectures will be these lecture notes (JP). Other useful books are Quantum Computation and Quantum Information by Nielsen and Chuang (NC), Classical and Quantum Computation by Kitaev, Shen, and Vyalyi (KSV), Quantum Computing Since Democritus by Aaronson, The Theory of Quantum Information by Watrous, and Quantum Information Theory by Wilde.

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

The first few weeks of the course will draw on material in Chapter 7 of the lecture notes and supplementary materials which will be provided.

Lectures:
March 30 and April 1: Lectures 1 and 2. Error correction review, erasure and correctability. 7.3, 7.10
April 6 and 8: Lectures 3 and 4. Cleaning lemma, bounds on local codes, string operators. 7.14, 7.19, 7.20
April 13: Lecture 5. Codes from circulant matrices and polynomials. Notes.
April 15: Lecture 6. Bivariate bicycle codes. Notes. Reference.
April 20: Lecture 7. Hypergraph product codes. Notes. Reference.
April 22: Lecture 8. Chain complexes and CSS codes. Notes.
April 27: Lecture 9. Lifted product codes. Notes. Reference.
April 29: Lecture 10. Syndrome decoding. Notes. Reference 1. Reference 2.
May 4: Lecture 11. Belief propagation. Notes.
May 6: No Lecture.
May 11: Lecture 12. Quantum computing by measurement. Notes.
May 13. Lecture 13. Pauli-based computation. Notes. Reference.

Homework assignments:
Problem Set 1, due 23 April. Local codes
Problem Set 2, due 7 May. Hypergraph products and lifted products
Problem Set 3, due 21 May. Syndrome decoding