MATH 6397: Special Topics
Quantum Information and Computation Theory
Spring 2024
"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
Monday, Wednesday, Friday 11:00-11:50am in F 154.
PGH 634
use Canvas to send email or use the email: anna@math.uh.edu please include MATH 6397 in the subject so that your email won't be regarded as spam
Office hours
My office hours for this course are Fridays 10-11am in
PGH 634. If you cannot make this time and would like to
meet, please send me an email and we will arrange for
another time.
(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 
Monday, Wednesday, Friday 11:00-11:50am in F 154.Contact
Dr. Anna VershyninaPGH 634
use Canvas to send email or use the email: anna@math.uh.edu please include MATH 6397 in the subject so that your email won't be regarded as spam
Office hours
My office hours for this course are Fridays 10-11am in
PGH 634. If you cannot make this time and would like to
meet, please send me an email and we will arrange for
another time.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 Complex 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 (qubits, gates, channels)
-Universal quantum computation
-Quantum teleportation and other protocols
-Quantum error-correction
-Noisy quantum channels
-Quantum algorithms (Shor's algorithm, Grover's algorithm)
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:
Homework
Research
Assignment
Instead of a homework you are welcome to write a 2-3 page
review article on any of the topics below. You must
inform me of your decision to do so before February 5th.
The deadline to submit the review article is two weeks before the last day of the class, i.e. April 12th.
If you need any advise, guidance, or a read over at any time during the semester, please let me know.
-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 Complex 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 (qubits, gates, channels)
-Universal quantum computation
-Quantum teleportation and other protocols
-Quantum error-correction
-Noisy quantum channels
-Quantum algorithms (Shor's algorithm, Grover's algorithm)
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: - 70% one of the two choices: You must inform me of your choice before February 5th.
- homework (completion only);
- review article with brief class presentation;
- 30% attendance
Homework 
There will be 4 homework assignments.
| Number |
Wilde book | Deadline |
| Homework 1 |
Chapter 3, Exercises: 3.3.2, 3.3.4, 3.3.6, 3.3.10, 3.3.11, 3.5.3, 3.5.4, 3.5.5, 3.5.6, 3.5.7, 3.6.1 |
Feb 5 |
| Homework 2 |
6.2.5, 6.5.1 Write the state after each step in 1) qudit super-dense coding protocol (Chapter 6.5.2) 2) qudit quantum teleportation protocol (Chapter 6.5.3) 3) coherent teleportation protocol (Chapter 7.4) 4.1.3, 4.1.4, 4.1.5, 4.1.9, 4.3.8, 4.3.16, 4.7.1, 4.7.3, 4.7.5, 4.7.9 |
March 4 |
| Homework 3 |
Nielsen and Chuang: 5.4, 5.5, 5.7, 5.10, 5.11, 5.12, 5.13 |
April 1 |
| Homework 4 |
9.1.3, 9.1.5, 9.2.3, 9.2.5, 11.4.1, 11.6.8, 11.8.6, 11.8.7 | April 26 |
Research
Assignment 
Instead of a homework you are welcome to write a 2-3 page
review article on any of the topics below. You must
inform me of your decision to do so before February 5th. The deadline to submit the review article is two weeks before the last day of the class, i.e. April 12th.
If you need any advise, guidance, or a read over at any time during the semester, please let me know.
| 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 |
| 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 |
Class Calendar
(this calendar is preliminary, and will be updated
as the term progresses)
| Monday | Wednesday | Friday |
| Jan 17 Introduction+Overview  |
Jan
19 Mathematical Background |
|
| Jan 22 Mathematical Background |
Jan 24 Noiseless Quantum Theory Nielsen, Chuang 2.1-2.2 Wilde 3 |
Jan 26 Noiseless Quantum Theory Nielsen, Chuang 2.1-2.2 Wilde 3 |
| Jan 29 Quantum Gates Nielsen, Chuang 4.1-4.3 |
Jan 31 Quantum Gates Nielsen, Chuang 4.1-4.3 |
Feb 2 Quantum Gates Nielsen, Chuang 4.4-4.5 |
| Feb 5 Quantum Protocols Wilde 6 |
Feb 7 Bring Laptop IBM Quantum |
Feb 9 Quantum Protocols Wilde 6-7 |
| Feb 12 Quantum Protocols Wilde 6-7 |
Feb 14 Homework 1 Discussion Noisy Quantum Theory Wilde 4.1-4.3 Nielsen, Chuang 2.4, 8.1-8.3 |
Feb 16 Noisy Quantum Theory Wilde 4.1-4.3 Nielsen, Chuang 2.4, 8.1-8.3 |
| Feb 19 Noisy Quantum Theory Wilde 4.1-4.3 Nielsen, Chuang 2.4, 8.1-8.3 |
Feb 21 No Class |
Feb 23 No Class |
| Feb 26 Noisy Quantum Channels+ Schwartz Decomposition Wilde 4.7, 5 Nielsen, Chuang 2.5 |
Feb 28 Purification Wilde 5 Nielsen, Chuang 2.5 |
March 1 Quantum Error Correction Nielsen, Chuang 10.3.3-10.3.4 |
| March 4 Quantum Error Correction Nielsen, Chuang 10.3.3-10.3.4 Progress report is due |
March 6 Quantum Error Correction Nielsen, Chuang 10.3.3-10.3.4 |
March 8 Homework 2 discussion |
| March 11 Spring break! |
March 13 |
March 15 Spring break! |
| March 18 Quantum Fourier Transform Nielsen, Chuang 5 |
March 20 Quantum Fourier Transform Nielsen, Chuang 5 |
March 22 Quantum Fourier Transform Nielsen, Chuang 5 |
| March 25 Order-finding, Factorization Nielsen, Chuang 5 |
March 27 Order-finding, Factorization Nielsen, Chuang 5 |
March 29 Quantum Search Algorithm Nielsen, Chuang 6 |
| Apr 1 Distance Measures Wilde 9 |
Apr 3 Distance Measures Wilde 9 |
Apr 5 Quantum Entropy Wilde 11 |
| Apr 8 Quantum Entropy Wilde 11 |
Apr 10 Quantum Entropy Inequalities Wilde 12 |
Apr 12 Quantum Entropy Inequalities Wilde 12 |
| Apr 15 Research Assignment Presentations |
Apr 17 Research Assignment Presentations |
Apr 19 Research Assignment Presentations |
| Apr 22 Research Assignment Presentations |
Apr 24 Research Assignment Presentations |
Apr 26
Research Assignment
Presentations
|
|
Apr 29
Research
Assignment Presentations
|
Congratulations! |