Bilkent Quantum Computing and Topology
Math 421

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.

Assessment methods - Fall 2022

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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

Dec 23: Math 521 presentation - Fall 2022.