Contact information

Instructor: Lin Lin
Lecture hours: TTh 9:30A-10:59A, Evans 748 (7th floor)
Office Hours: T 11AM-12PM, Evans 817
Course catalog: https://classes.berkeley.edu/content/2026-spring-math-275-002-lec-002


Update

Lecture notes:

https://math.berkeley.edu/~linlin/qasc/

2/19: Live notes updated Ch 14,15; Adding materials in Ch12 and 13
2/11: Live notes updated Ch 12,13,17; Fix problems in 5.4, 9.7
2/2: Live notes updated Ch 10,11,17
1/21: Live notes updated Ch 5 and 9
1/15: New lecture notes ("live notes") are uploaded. Please read Ch 1-2 for background materials.



Course description

Quantum computers have the potential to revolutionize how we think about computing. Central to quantum computation are quantum algorithms, which often differ considerably from classical algorithms. This is an advanced graduate course course that introduces quantum algorithms essential for scientific computation. Topics include phase estimation, Hamiltonian simulation, block encoding, quantum singular value transformation, and their applications in tasks like solving linear systems, eigenvalue problems, and differential equations. The focus is on algorithmic components, design, and analysis. The quantum algorithms discussed are largely independent of the specific physical hardware on which they're implemented. Upon completing the course, students will have a solid understanding of the primary quantum algorithmic techniques for scientific computation and will be prepared to engage with technical discussions and design novel quantum algorithms in their research.

Prerequisites

Due to the interdisciplinary nature of the topic, the course material requires a broad knowledge base. At a minimum, students should have a solid understanding of linear algebra, as well as basic knowledge of probability theory and quantum mechanics (all at the undergraduate level). Below is a reference list of relevant courses you may have taken or been exposed to:

  • Linear Algebra (MATH 54 / PHYSICS 89 / EECS 16A, or MATH 110)
  • Probability (MATH 55 / STAT 20 / CS 70)
  • Quantum Mechanics (PHYSICS 7C, PHYSICS 137A, or CHEM 120A), or Quantum Information Theory (CHEM/CS/PHYS 191, or CS 294-66)
Before the first class: please read Chapter 1 (Preliminaries of quantum computation) 1.1-1.6 of the Notes. Ensure that you either have prior knowledge of the material or can comprehend it upon reading.

Enrollment Instructor consent is not needed. However, undergraduate students need to submit Sp26 Graduate Enrollment Request Form to be granted a permission. Additionally, please also fill this Google form

Resources:

Evaluation

The formal grade evaluation will be entirely based on the final project. Details and guidelines for the project will be released during the semester.

Schedule

This is a tentative weekly schedule, subject to (likely) changes.
Ch refers to chapters in the "live notes"


The Content column may not be up to date and is revised every few weeks. Please refer to the Reading column for the most up-to-date information on which sections are covered in the class.


# Date Content Reading
1 Tue. 1/20 Course information. Review of background materials. Ch 1, Ch 2.2-2.6
2 Thu. 1/22 Block encoding 9.1
3 Tue. 1/27 Linear combination of unitaries 9.2-9.3
4 Thu. 1/29 Foundation: Quantum processing of classical information 5.1-5.4
Quanta (with podcast) on reversible computation
5 Tue. 2/3 Block encoding of sparse matrices 9.6-9.8, 10.1-10.2
6 Thu. 2/5 Qubitization 10.3-10.5
7 Tue. 2/10 Grover type algorithms 11.1-11.4
8 Thu. 2/12 Classical Markov chains and quantum walk 17.1-17.2
9 Tue. 2/17 Classical Markov chains and quantum walk 17.3-17.4
10 Thu. 2/19 Quantum signal processing and nonlinear Fourier transform 12.1-12.7
11 Tue. 2/24 Quantum singular value transformation 13.1-13.4
12 Thu. 2/26 Block encoding based Hamiltonian simulation 14.1-14.2
13 Tue. 3/3 Operator splitting based Hamiltonian simulation
14 Thu. 3/5 Foundation: perturbation theory Guest lecture by Dr. Ethan Epperly
15 Tue. 3/10 Operator splitting based Hamiltonian simulation
16 Thu. 3/12 Foundation: probability, density operator and quantum channel
17 Tue. 3/17 qDRIFT algorithm
18 Thu. 3/19 Foundation: distance measures Guest lecture by Dr. Jiaqing Jiang
19 Tue. 3/24 Spring break. No class.
20 Thu. 3/26 Spring break. No class.
21 Tue. 3/31 Quantum Fourier transform and quantum phase estimation
22 Thu. 4/2 Foundation: query lower bound
23 Tue. 4/7 Eigenvalue problems
24 Thu. 4/9 Linear systems of equations
25 Tue. 4/14 Differential equations
26 Thu. 4/16 Open quantum systems
27 Tue. 4/21 Project presentation.
28 Thu. 4/23 TBD
29 Tue. 4/28 Project presentation.
30 Thu. 4/30 Project presentation.