MATH 6397: Special Topics
Quantum Computation Theory
Spring 2020
- Due to COVID-19
situation, UH has canceled classes during the week of March 16,
and moved all classes after that to a remote setting. Starting
March 23, every week you will receive a reading material with an
assignment to complete while you are reading. All other
assignments, such as homework 3,4 and a review article are
canceled. Please write up everything you have on your review
article and send it to me.
"In mathematics, you don't understand
things, you just get used to them."
John von Neumann
All information on the website is subject to change if circumstances require it. I will communicate any changes during the class. Check back for the most up-to-date information.
If you haven't found here what you were looking for, please contact me using the contact information below, or let me know in person. All your inputs are highly valued and appreciated.
Class Place/Time
Tuesday, Thursday 11:30-1:00am in F 154
anna@math.uh.edu
please include MATH 6397 in the subject so that your email won't be regarded as spam
Presentation to Middle Schoolers
(this
calendar is preliminary, and will be updated as the term progresses)
John von Neumann
All information on the website is subject to change if circumstances require it. I will communicate any changes during the class. Check back for the most up-to-date information.
If you haven't found here what you were looking for, please contact me using the contact information below, or let me know in person. All your inputs are highly valued and appreciated.
Class Place/Time 
Tuesday, Thursday 11:30-1:00am in F 154Contact
Dr. Anna Vershyninaanna@math.uh.edu
please include MATH 6397 in the subject so that your email won't be regarded as spam
Text
Lecture notes will be provided to
you every class.
For personal reference, you may look
at the following books:
-Michael Nielsen and Isaac Chuang,
"Quantum computation and quantum information", Cambridge university
press, 2010
-Mark Wilde, "From Classical to Quantum Shannon Theory" arXiv:1106.1445
You do not need to purchase either of these books. I can recommend any additional books if you request it, which you may borrow from my office.
-Linear Algebra
-Basics of Probability
-Basics of Functional Analysis
It is not expected that you know any quantum mechanics, computer science, of information theory before the start of the class.
Course Overview
-Basics of quantum mechanics
-Universal quantum computation
-Quantum teleportation and other protocols
-Quantum error-correction
-Noisy quantum channels
-Quantum complexity
-Quantum algorithms
This list is subject to change depending on time constrains etc. Check the calendar below for the most up-to-date information.
Grading
Your final grade will break down as follows: the grading scheme
has been changed on March 16th due to shifting to remote
learning.
Homework
Research
Assignment
Instead of a homework you are welcome to write a 3-4 page
review article on any of the topics below. You must inform me
of your decision to do so before February
4. The deadline
to submit the review article is the week before the last day of the
class, i.e. April
16.
If you need any advise, guidance, or a read over at any time during
the semester, please let me know. We will discuss these assignments
during the last class, you must be prepared to briefly present your
paper.
-Mark Wilde, "From Classical to Quantum Shannon Theory" arXiv:1106.1445
You do not need to purchase either of these books. I can recommend any additional books if you request it, which you may borrow from my office.
Prerequisites
For this course it will be expected that you know the following material well:-Linear Algebra
-Basics of Probability
-Basics of Functional Analysis
It is not expected that you know any quantum mechanics, computer science, of information theory before the start of the class.
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Course Overview 
During the course we aim to cover the following topics:
-Basics of quantum mechanics
-Universal quantum computation
-Quantum teleportation and other protocols
-Quantum error-correction
-Noisy quantum channels
-Quantum complexity
-Quantum algorithms
This list is subject to change depending on time constrains etc. Check the calendar below for the most up-to-date information.
Grading
Your final grade will break down as follows: the grading scheme
has been changed on March 16th due to shifting to remote
learning. - 40% one of the three choices: You must inform me of your choice before February 4.
- homework;
- review article;
- presentation to middle schoolers about quantum
computer/computation/theory/...
- 10% attendance until Spring Break
- 50% weekly assignments after Spring Break
Homework
There will be 4 homework assignments. One question on each of the homework sets will be to write a two-three sentences summarizing the most interesting news story in quantum computation/information/physics since the last homework. One source of the news is the ORNL Quantum Communication Institute, which you can subscribe to using this link. Another is Quanta Magazine or MIT Technology Review. You may use any other source of information. The news that you summarize must be related to quantum communication or physics.
| Number |
Deadline |
| Homework
1 |
Feb 4 |
| Homework
2 |
March 5 |
| Homework 3 |
canceled |
| Homework 4 |
canceled |
Research
Assignment 
Instead of a homework you are welcome to write a 3-4 page
review article on any of the topics below. You must inform me
of your decision to do so before February
4. The deadline
to submit the review article is the week before the last day of the
class, i.e. April
16.
If you need any advise, guidance, or a read over at any time during
the semester, please let me know. We will discuss these assignments
during the last class, you must be prepared to briefly present your
paper.Update: You
should stop working on your review article on March 16th. Write up
everything you have so far and send it to me before March 30th.
| Topic |
Reading |
| Quantum computers. Who has of what kind? Their advantages, disadvantages and limitations. |
Research devices by: IBM,
Intel, Google, D-Wave, various Universities,... Hardware: quantum dot, quantum spin, ion trap, superconductor, cavity QED, optical lattices Theoretical models: quantum circuit, adiabatic computation, one-way computation, topological quantum computation Review paper |
| Applications of quantum
computers. What problems can they solve? Atomic clocks, quantum biology, quantum sensors, lasers, GPS, quantum gravity... |
D-Wave,
Microsoft,
find at least one other reference (research at least two
applications) Review paper 1 Review paper 2 q. biology + quantum Bitcoin mining + graviton |
| Imperfect quantum cloning. Does it imply imperfect FTL communication? |
paper
1 + paper
2 |
| Problem of Time |
Wiki
+ paper
1 (p. 1-3)+ paper
2 (ch. 1-3) |
| Black hole paradox | Wiki
+ paper
(lecture 6) |
| Student's choice |
Discuss your topic with Dr. Vershynina |
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Presentation to Middle Schoolers
As a third choice you can prepare a presentation and hands on activity suitable for middle schoolers and deliver it during one of the CHAMP meetings. Two of the weekly meetings are happening on the schools campuses (5-10 min away), and you will be provided with transportation to and from the UH campus. There are 12 academically advanced kids in each school group from undeserved neighborhoods. The meeting times are:
Tuesday 10:00-11:00am
Tuesday 2:00-3:00pm
Another meeting is happening every other week on the UH campus for home schooled children. There are 15 kids in that group. The meeting times are:
Fridays 9:30-11:15am in PGH 646A, every other week, see here for dates.
You need to deliver presentation and activity only for one hour in any of these meetings. You will be assisted by the Leaders of these meetings. If you need help coming up or developing a presentation and/or an activity, please let me know. You must inform me of your choice to make a presentation to children before February 4.
Class Calendar
(this
calendar is preliminary, and will be updated as the term progresses)
| Jan
14 Introduction+Overview  |
Jan
16 Mathematical Background+ Noiseless Quantum Theory Nielsen, Chuang 2.1-2.2 Wilde 3 |
Jan
21 Noiseless Quantum Theory |
Jan
23 Quantum Gates Nielsen, Chuang 4.1-4.3 |
| Jan
28 Quantum Gates Nielsen, Chuang 4.4-4.5 |
Jan
30 Quantum Protocols Wilde 6 |
Feb
4 Homework and news discussion IBM Q-Experience Meeting in the library 300G HW deadline |
Feb
6 Class is canceled - I'm
at the conference
 |
| Feb
11 Noisy Quantum Theory Wilde 4.1-4.3 Nielsen, Chuang 2.4, 8.1-8.3 |
Feb
13 Schwartz Decomposition+Purification Wilde 5 Nielsen, Chuang 2.5 |
Feb
18 Scott Aaronson's Physics colloquium Tuesday 2:30-3:30pm SR1 634 |
Feb
20 Scott Aaronson's Math colloquium +student talk Wednesday 1:30-2:30pm 3:00-4:00pm PGH 646A |
| Feb
25 Class is canceled - I'm on the NSF panel 
|
Feb
27 Class is canceled - I'm on the NSF panel |
March
3 Overview of the class |
March
5 Quantum Error Correction Nielsen, Chuang 10.3.3-10.3.4 HW deadline |
| March
10 Spring break! |
March
12 |
March
17 No classes! Stay safe! |
March
19 No classes From now on, our class has moved to a remote setting |
| March
24 Complexity |
March
26 Complexity |
March
31 Quantum Fourier Transform Nielsen, Chuang 5 |
Apr
2 Quantum Fourier Transform Nielsen, Chuang 5 |
| Apr
7 Order-finding, Factorization Nielsen, Chuang 5 |
Apr
9 Order-finding, Factorization Nielsen, Chuang 5 |
Apr
14 Quantum Search Algorithm Nielsen, Chuang 6 |
Apr
16 Quantum Search Algorithm Nielsen, Chuang 6 |
| Apr
21 Review |
Apr
23 Review |
Congratulations!
 |
 |
