Introduction to Quantum Computing
CSE 190 / Math 152 - Spring 2025
| Place and Time: | Podemos 1A20, TTh 2:00pm-3:20pm |
| Instructor: | Daniel Grier (dgrier@ucsd.edu) |
| Course staff: | Jack Morris (jrm035@ucsd.edu), Ryan Batubara (rbatubara@ucsd.edu) |
| Resources: | Canvas, Gradescope, Piazza |
| Daniel's office hours: | Thursday from 3:30pm-4:30pm in APM 7141 |
| Jacks's office hours: | Tuesday from 11am-12pm in CSE B250A |
| Ryan's office hours: | Monday from 3pm-4pm in APM 5829 |
- Homework 1 - due April 8th at 1:30pm
- Homework 2 - due April 16th at 11:59pm
- Homework 3 - due April 24th at 11:59pm
- Homework 4 - due May 7th at 11:59pm
- Homework 5 - due May 23rd at 11:59pm
- Homework 6 - due June 6th at 11:59pm
These lecture notes cover all material for this class. They will be updated throughout the quarter (last updated: 6/1/25). I have also included links to these excellent notes by John Watrous for a different perspective on many of the topics.
| Lecture 1 | Introduction to quantum bits and quantum operations | 1.1, pg 1-5 |
| Lecture 2 | Multiple qubits, entanglement, and tensor products | 1.2, pg 1-4 |
| Lecture 3 | Properties of tensor products | 1.2, pg 3-5 |
| Lecture 4 | Partial measurement, Dirac notation, Inner/outer products | 1.3, pg 6-8 |
| Lecture 5 | Inner products, No-cloning theorem, quantum circuits | 1.5, 2.1, pg 7-8 |
| Lecture 6 | Circuit identities, controlled-operations | 2.1, pg 2-5 |
| Lecture 7 | Query complexity and Deutsch's algorithm | 3.1, pg 3-6 |
| Lecture 8 | Deutsch's algorithm continued, Deutsch-Jozsa problem | 3.2, pg 3-6 |
| Lecture 9 | Deutsch-Jozsa algorithm | 3.2, pg 3-6 |
| Lecture 10 | Bernstein-Vazirani, Fourier sampling, Simon's problem | 3.2, pg 1-5 |
| Lecture 11 | Simon's algorithm | 3.3, pg 1-5 |
| Lecture 12 | Role of structure in quantum speedups | 3.4 |
| Lecture 13 | Grover's algorithm | 3.4, pg 1-6 |
| Lecture 14 | Grover's algorithm, manipulating integers using qubits | 3.4, 4.1, pg 1-6 |
| Lecture 15 | Shor's algorithm, order finding, and Simon's problem revisited | 4.2, 4.3, pg 5-7 |
| Lecture 16 | QFT and Simon's period finding algorithm | 4.3, A.3, pg 5-7 |
| Lecture 17 | Quantum algorithm for ordering finding | 4.4, pg 1-5 |
This is an advanced undergraduate course focusing on the mathematical theory of quantum computers. The course will start with a general introduction to quantum computers: How do we mathematically specify a quantum state? What kinds of operations can we apply to a quantum state? How can we measure quantum states to solve computational problems? After having developed these basics, we will learn how to construct and analyze quantum algorithms, including those that have generated some of the most excitement about the future of quantum computing.
Prerequisites: A previous course in linear algebra is required (Math 18, Math 20F, or Math 31AH). All previous math experience will be very helpful, especially discrete math (Math 15A, CSE 20), probability (Math 11, CSE 21), and complex numbers. No prerequisite knowledge of physics or quantum computation is required.
- Foundations: states, operations, measurements
- Quantum information: entanglement, no-cloning theorem
- Circuits: gates, universality, measures of complexity, programming
- Algorithms: Deutsch-Jozsa, Simon, Grover, quantum Fourier transform
- Complexity: classical simulation, quantum computational advantage
- Homework (30%): There will be 6 homework assignments throughout the quarter. The lowest homework grade will be dropped. You are allowed to turn homeworks assignments in 1-day late for a 25% penalty. No other late submissions will be accepted.
- Participation (10%): Participation is based entirely on online quizzes on Gradescope given both synchronously and asynchronously. Your lowest 3 quiz scores will be dropped.
- Midterm (25%): Date - May 1st in class. There is no make-up midterm.
- Final (35%): Date - June 10th at 3pm during finals week. If final grade is higher than midterm, it will replace the midterm grade.
Following UCSD (and common) practice recommended by the Academic Integrity Office, assessments, especially those given at non-overlapping times, will be comparable, but may not be identical. This practice is meant to maintain course integrity, avoiding non-allowed collaboration (either intentional or accidental).