# Introduction to Quantum Computation

This is the homepage of Math 421/521 Introduction to Quantum Computation offered in Spring 2021 at Bilkent University.

Instructor: Cihan Okay

Location: Zoom

Time: Mon 9:30-10:20, Wed 13:30-15:20

Grading scheme for Math 421: Take-home midterm (HW2) - %25, Final - %20, Homework (HW1-3-4 each %16) - %48, Attendance - %7

Grading scheme for Math 521: Take-home midterm (HW2) - %20, Final - %20, Homework (HW1-3-4 each %15) - %45, Oral presentation and report - %15

### 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).

Reading suggestions for a general overview:

Chapter I (1.1–1.6) from John Preskill’s lecture notes

Chapter I (1.1–1.5) from Nielsen–Chuang

Reader-friendly background reference sources:

Linear algebra done right by Sheldon Axler

Probability and random processes by Geoffrey Grimmett and David Stirzaker

Introduction to the theory of computation by Michael Sipser

Quantum computing resources other than the textbook:

Preskill’s online lecture notes

Quantum Computing since Democritus by Scott Aaronson

Quantum Computer Science: An Introduction by David Mermin

An Introduction to Quantum Computing by Phillip Kaye, Raymond Laflamme, Michele Mosca

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

### Weekly syllabus

Week 1 (Jan 27): Dirac notation, Inner product spaces, Linear operators

Week 2 (Feb 1): Eigenvectors and eigenvalues, Spectral decomposition

Week 3 (Feb 8): Polar and singular value decomposition, Postulates of quantum mechanics

Week 4 (Feb 15): Quantum measurements

Homework 1Week 5 (Feb 22): Applications: teleportation and superdense coding

Week 6 (Mar 1): Density operators

Week 7 (Mar 8): Schmidt decomposition, Bell inequalities

Homework 2: Take-home midtermWeek 8 (Mar 22)1: Models of computation: Turing machines, Circuits

Week 9 (Mar 29): Computational complexity

Week 10 (Apr 5): Quantum circuits, Universal quantum gates

Homework 3Week 11 (Apr 12): Quantum computational complexity, Quantum algorithms: Deutsch–Josza algorithm, Simon’s algoritm

Week 12 (Apr 19): Quantum Fourier transform, Phase estimation

Week 13 (Apr 26): Order-finding and Shor’s factoring algorithm

Homework 4Week 14 (May 3): Presentations: only Math 521, though everyone can attend.

Final: Time and Location will be announced.

### Lecture notes

Lecture 1 - Linear algebra in Dirac notation (Last revised: Mar 10)

Lecture 2 - Postulates of quantum mechanics (Last revised: Mar 10)

Lecture 3 - Computational models (Last revised: Apr 5)

Lecture 4 - Quantum circuits (Last revised: Apr 14)

Lecture 5 - Quantum algorithms (Last revised: May 5)