Introduction to Quantum Computing
CSE 190 / Math 152

Place and Time:FAH 1450, TTh 2:00pm-3:20pm
Instructor:Daniel Grier (dgrier@ucsd.edu)
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 we can 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
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.