# Introduction to Quantum Computation

This is the homepage of Math 421/521 Introduction to Quantum Computation, offered in Fall 2022 at Bilkent University.

Instructor: Cihan Okay

Location: SA Z04

Time: Tue 8:30-10:20, Thu 13:30-15:20

Tuesdays 8:30-9:20 are for Qiskit lectures.

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

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

### Textbook and other reading

Textbook of the course 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

For more see Math-421 Spring 2021.

# Weekly syllabus

### Linear Algebra

Week 1 (Sep 15): Inner product spaces

Week 2 (Sep 20-22): Tensor product, Dirac notation

Week 3 (Sep 27-29): Spectral decomposition, Polar and singular value decomposition

Lecture notes: M421-L1

### Quantum theory

Week 4 (Oct 4-6): Axioms of quantum mechanics

Week 5 (Oct 11-13): Teleportation and superdense coding

Week 6 (Oct 18-20): Density operators

Week 7 (Oct 25)1: Bell inequalities

Lecture notes: M421-L2

### Theory of computation

Week 8 (Nov 1-3): Turing machines, Circuits

Week 9 (Nov 8-10): Computational complexity

Week 10 (Nov 15-17): Quantum circuits, Universal quantum gates

Week 11 (Nov 22-24): Quantum computational complexity

Lecture notes: M421-L3

### Quantum algorithms

Week 12 (Nov 29-Dec 1): Deutsch–Jozsa algorithm, Simon’s algoritm

Week 13 (Dec 6-8): Quantum Fourier transform, Phase estimation

Week 14 (Dec 13-15): Order-finding, Shor’s factoring algorithm

Week 15 (Dec 20-22): Hidden subgroup problem

Lecture notes: M421-L4