#
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

### Grading Information:

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