Quantum Computing. 18.435 / 2.111. Fall 2006
Prerequisites:
Understanding of linear algebra.
Book:
I recommend the book of Nielsen and Chuang, and will be using
it to prepare some of my lectures with. There is also an excellent set of
lecture notes from John
Preskill's course online.
You can see the webpages for the 2003 and
2005 versions of this class on the
web.
Office hours:
-
My office hours are
- Wednesday, 10:30-12:00, Room 2-369
- email: shor@math.mit.edu
- On November 22, the day before Thanksgiving, all office hours are cancelled.
-
Andrew Fletcher's office hours are
- Wednesday, 1:00-3:00, 32-044E (basement of Stata center).
- email: fletcher@mit.edu
- On November 22, the day before Thanksgiving, all office hours are cancelled.
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
- Implementations of quantum computers
-
- Quantum error correcting codes
- Quantum cryptography
- Quantum fault tolerance
Tutorial/Recitation:
There is a "recitation" listed in the catalog. It's not really a
recitation; it's a tutorial, and I expect I'm not going to hold more than
five of them. The purpose of this is to help students who haven't had any
quantum mechanics (or who have, but haven't seen it from this angle) catch
up with the rest of the class. There won't be one Monday the 11th, but
there will be at 2:30 in room 1-132 on Sept. 18, Oct. 2, and Oct. 16.
There will also be one in my office 2-369 on Friday, October 6, at 2pm.
There will be no tutorial on Monday, October 23.
Grading Information:
I will give one in-class quiz, which will make up 30% of the grade.
This will be on October 31.
Homework assignments will determine 70% of the grade.
There will be weekly homework, most of the problems will be fairly easy,
although I plan to put one or two harder problems on each homework assignment.
I find that doing examples really helps to see what is going on in quantum
computation, so I'm not making you do all these matrix manipulations just to
torment you.
This year I am going to be doing something different with the homework.
The last two problem sets are going to be longer, will cover the entire
term, and will count more than the rest of the assignments.
These last two homework assignments will count roughly double the
normal ones, and so probably comprise around 12% of the grade
each.
Homework Assignments
The first homework assignment is here.
Due on Sept. 21st.
Solutions are now here.
The second homework assignment is here. Due on Sept. 28th.
Solutions are now here.
The third homework assignment is here. Due
on October 5th.
Solutions are now here.
The fourth homework assignment is here.
Solutions are now here.
Question number 1 (change of basis) could actually be interpreted two ways,
so both the matrices given in the solutions and their adjoints are valid
solutions. If you believe your solution was graded improperly, please talk
with the TA, Andrew Fletcher.
The fifth homework assignment is here.
Solutions are now here.
Due Thursday, Oct. 19
The sixth homework assignment is here.
Solutions are now here.
Due Thursday, Oct. 26
The seventh homework assignment is
here. Due Thursday, Nov. 9
Solutions are now here.
The eighth homework assignment is
here. Due Thursday, Nov. 16
Some typos are now fixed.
Solutions are now here.
The ninth homework assignment is
here. Due Thursday, Nov. 30
Solutions are now here.
The tenth (and next to last) homework assignment is
here. Due Thursday, Dec. 7
Solutions are now here.
The last homework assignment is
here. Due Thursday, Dec. 14
It can be turned in at the TA's (Andrew Fletcher's) office, or
emailed to him, or brought to class on Tuesday, Dec. 11.
Lectures
I will try to announce the sections of Nielsen and Chuang (NC) or Preskill
that contain the material we're covering here. I'm not following
the book exactly, so I will 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.
I'm also posting a brief summary of the lectures.
Since I know Nielsen and Chuang better, I'm giving the sections from NC
(and leaving out Preskill's notes, which are excellent) unless NC doesn't
cover it.
-
Thur. 09/07:
- NC 3.1.2 to 3.2.3;
-
Tues. 09/12:
- NC 3.2.5; 2.2.1; 2.2.2; 4.2;
-
Thur. 09/14:
- NC 2.2.3 to 2.2.5; 4.2; 2.2.7, 2.2.8
-
Tues. 09/19:
- NC 2.6; 1.3.6
-
Thurs. 09/21:
- NC 1.3.5, 2.3, 1.3.7, 2.6 (no-cloning theorem, superdense coding,
teleportation)
-
Tues. 09/26:
- NC 2.2.5, 2.2.6, 4.1, 4.2, 4.3; projective measurements
and POVM's, and the circuit model of quantum computing, part I.
-
Thurs. 09/28:
- NC 4.4, 4.5; gates for the circuit model.
-
Tues. 10/03:
- NC 4.4, 4.5; more gates for the circuit model.
-
Thurs. 10/05: (notes not here yet)
- Simon's algorithm. Not in NC. See Preskill 6.3, pp. 43-45.
-
Thurs. 10/12:
(notes not here yet)
- the quantum Fourier transform. NC 5.1, 5.2
-
Tues. 10/17:
(notes not here yet)
- Phase estimation and factoring. NC 5.3, 5.4
-
Thurs. 10/19:
(notes not here yet)
- Last piece of factoring (reduction from phase estimation to
periodicity), discrete logarithms. Hidden subgroup
problem.
-
Tues. 10/24:
(notes not here yet)
- Grover's algorithm.
-
Thur. 10/26:
(notes not here yet)
- More on Grover's algorithm/review for exam.
-
Thur. 11/2:
(notes not here yet)
- Operators x and p for quantum mechanics on the line.
-
Tues. 11/7:
(notes not here yet)
- The harmonic oscillator.
-
Thurs. 11/9:
(notes not here yet)
- Density matrices and quantum operations.
-
Tues. 11/14:
(notes not here yet)
- Guest lecture (Seth Lloyd): electromagnetic resonance.
-
Thurs. 11/16:
(notes not here yet)
- More on density matrices and quantum operations.
-
Tues. 11/21:
(notes not here yet)
- Lecture on
Peres-Wootters and the discovery of
teleportation.
-
Tues. 11/28:
(notes not here yet)
- Quantum error-correcting codes
NC 10.1-10.3
-
Thurs. 11/30:
(notes not here yet)
- Quantum error-correcting codes
NC 10.4
Tues. 12/03:
(notes not here yet)
- Quantum cryptography
NC 12.6
Thurs. 12/05:
(notes not here yet)
- Quantum fault tolerance, part 1
NC 10.6
Thurs. 12/05:
(notes not here yet)
- Quantum fault tolerance, part 2
NC 10.6