# Quantum Computing. 18.435 / 2.111. Fall 2003

### Prerequisites:

Understanding of linear algebra.

### Topics to be covered include:

• (Just) enough quantum mechanics to understand quantum computation.
• Quantum algorithms.
• Simon's algorithm
• The prime factorization algorithm
• Grover's search algorithm
• Mathematical models of quantum computation, their relationships to each other, and to physical systems.
• Quantum error correcting codes
• Quantum cryptography
• Quantum fault tolerance

I will give two quizzes, which will make up 30% of the grade. Homework assignments will determine 70% of the grade.
The first quiz will be on October 23.
The second quiz will be on December2.

#### Homework Assignments

The first homework assignment is here. Solutions are here.

The second homework assignment is here. Solutions are here.
WARNING: I made a mistake in the second homework assignment. Both exponentials in problem number 4 should be e^(i theta). This unfortunately means that problem 5 is now impossible, so you don't have to do that one.

The third homework assignment is here. Solutions are here.

The fourth homework assignment is here.
Solutions are here.
NOTE: There is a typo in the second problem. The quantum state should be
1/2 (|0000>+|0101>+|1010>-|1111>).

The fifth homework assignment is here.
Solutions are here.

### Lectures

I will try to announce the chapters of Nielsen and Chuang that contain most of the material we're covering here. I'm not following the book exactly, so I may skip over some material from these chapters, and may include some extra material, but for those who want to look at the textbook before class, this will give an idea of what I'll be covering. Scribe notes to many of the lectures are avaialble here. Scribe notes available
Thur. 09/04:
Introduction and Overview
Tues. 09/09:
Sections 2.1, 2.2
Thur. 09/11:
Sections 2.2, 2.6
Tues. 09/16:
Sections 3.1, 3.2.5, 4.2-4.6
Thur. 09/18:
Sections 4.2-4.6, 1.4-1.4.4
Tues. 09/23:
Sections 5.1-5.4
Thur. 09/25:
Sections 5.1-5.4
Tues. 09/30:
Sections 5.1-5.4
Thur. 10/02:
Sections 5.1-5.4
Tues. 10/07:
Section 6
Thur. 10/09:
Section 6 (I originally planned to use some material from quant-ph/0005055 in this lecture, but decided against it.)
Tues. 10/14:
Sections 1.3.6, 1.3.7, 2.3
Thur. 10/16:
Models for quantum computation
Tues. 10/21:
Computing with cluster states: This material (some of it presented differently) can be found in quant-ph/0301052
Tues. 10/28:
More computing with cluster states.
Thur. 10/30:
We'll start quantum error correcting codes: 10.1-10.2, 10.3.1,
Tues. 11/4:
Now, we have to go back to tell you more about quantum mechanics. This is so we can deal with noise in quantum error correcting codes. In several lectures, we will cover 2.4, 2.5, 8.1, 8.2.
Thur. 11/6:
More about quantum mechanics. We'll talk about Hamiltonians, how to get unitary transformations, and the harmonic oscillator
Thur. 11/13:
Guest lecture by Ike Chuang on implementations of quantum computing
Tues. 11/18:
Quantum CSS codes, 10.4, 10.3.3
Thurs. 11/20:
More on quantum error correcting codes.
Tues. 11/25:
Quantum cryptography, 12.6
Thurs. 12/04:
Fault tolerance 10.6
Tues. 12/09:
Fault tolerance 10.6