Introduction to Quantum Computing
CSE 190 / Math 152

Place and Time:FAH 1450, TTh 2:00pm-3:20pm
Instructor:Daniel Grier (dgrier@ucsd.edu)
TA:Sihan Liu (sil046@ucsd.edu)
Course materials:Canvas, Gradescope, Piazza

Daniel's office hours:Thursday from 3:30pm-4:30pm in CSE 4218
Sihan's office hours:Monday from 2:30pm-3:30pm in CSE B260A

Assignments

Lecture 1 Introduction to quantum bits and quantum operations reading materials
Lecture 2 Quantum systems with many qubits and tensor products reading materials
Lecture 3 Entanglement, tensor products of unitaries, and Dirac notation reading materials
Lecture 4 Dirac notation, no cloning theorem, and circuits pg 6-8, pg 55-56
Lecture 5 Quantum circuits, gate sets, and controlled-operations pg 2-5
Lecture 6 Controlled unitaries and partial measurement pg 4-8
Lecture 7 Query complexity and Deutsch's algorithm pg 3-6
Lecture 8 Deutsch-Jozsa algorithm pg 3-6
Lecture 9 Simon's algorithm pg 1-5
Lecture 10 Grover's algorithm pg 1-6, pg 1-5
Lecture 11 Quantum Fourier Transform pg 4-6
Lecture 12 Quantum Fourier Transform continued, phase estimation pg 1-6, pg 4-6
Lecture 13 Kitaev phase estimation, reducing factoring to order finding pg 3-4

Overview

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.

Textbook: All content will be covered in lectures. There is no official textbook nor will there be a set of canonical lecture notes. That said, most of what will be taught in class is covered in one of the following sources, all of which can be accessed freely online:

The plethora of excellent expository material out there means that if you're having trouble understanding something in one set of notes, try another which might explain things more intuitively to you. If you'd like to purchase a physical textbook, my personal favorite is the excellent Quantum Computation and Quantum Information by Nielsen and Chuang. If you can't find a reference for something we've covered in class, please reach out.

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.

Topics
  • 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
Evaluation
  • Homework (30%): There will be 6-7 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 2nd in class. There is no make-up midterm.
  • Final (35%): Date - June 11th at 3pm during finals week. If final grade is higher than midterm, it will replace the midterm grade.
Accommodations
Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities. Students are required to discuss accommodation arrangements with instructors and OSD liaisons in the department in advance of any exams or assignments.