Bilkent Quantum Computing and Topology
Math-421 Spring 2021

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

Assessment methods

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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).

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 1

• Week 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 midterm

• Week 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 3

• Week 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 4

• Week 14 (May 3): Presentations: only Math 521, though everyone can attend. See Math 521 presentation
  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)

Questions & answers