# Introduction to Quantum Computation

This is the homepage of Math 421/521 Introduction to Quantum Computation, offered in Fall 2024 at Bilkent University.

Instructor: Cihan Okay

Location: G-236

Time: Tue 11:30-12:20, Thu 15:30-17:20

### Textbook and other reading

Lecture notes: Sept 7, 2024

The course textbook is Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang, Cambridge University Press (10th Anniversary edition).

Reader-friendly sources for background:

Linear algebra done right by Sheldon Axler

Introduction to the theory of computation by Michael Sipser

Quantum computing/information resources other than the textbook:

Classical and quantum computation by Alexei Kitaev, Alexander Shen, Mikhail N. Vyalyi

The theory of quantum information by John Watrous

Also see Math-421 Fall 2022 and Math-421 Spring 2021.

# Weekly Syllabus

### Linear Algebra

Week 1 (Sep 17-19): Inner product spaces

Week 2 (Sep 24-26): Tensor product, Dirac notation

Week 3 (Oct 1-3): Spectral decomposition, Polar and singular value decomposition

### Quantum theory

Week 4 (Oct 8-10): Axioms of quantum mechanics

Week 5 (Oct 15-17): Teleportation and superdense coding

Week 6 (Oct 22-24): Density operators

Week 7 (Oct 31)1: Bell inequalities

### Theory of computation

Week 8 (Nov 5-7): Turing machines, Circuits

Midterm (Nov 9, 11:00-13:30)

Week 9 (Nov 12-14): Computational complexity

Week 10 (Nov 19-21): Quantum circuits, Universal quantum gates

Week 11 (Nov 26-28): Quantum computational complexity

### Quantum algorithms

Week 12 (Dec 3-5): Deutsch–Jozsa algorithm, Simon’s algorithm

Week 13 (Dec 10-12): Quantum Fourier transform, Phase estimation

Week 14 (Dec 17-19): Order-finding, Shor’s factoring algorithm

Week 15 (Dec 24): Hidden subgroup problem

Grading Scheme

Math 421: Midterm - %25, Final - %30, Homework (4 assignments) - %40, Attendance - %5

Math 521: Midterm - %25, Final - %25, Homework (4 assignments) - %40, Oral presentation - %10