MATH 6395: Special Topics
Quantum Information Theory
Fall 2018
the course is finished - enjoy your break!
"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 10:00-11:30am in M 119
anna@math.uh.edu
please include “MATH 6395” in the subject so that your email won't be regarded as spam
-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 buy either of these books.
-Linear Algebra
-Basics of Probability
-Basics of Functional Analysis
It will not be expected that you know any quantum mechanics, computer science, information theory.
Course Overview
During the course we aim to cover the following topics:
-Basics of quantum mechanics
-Universal quantum computation
-Quantum teleportation
-Quantum error-correction
-Entropy and quantum information
-Noisy quantum channels
This list is subject to change depending on time constrains etc. Check the calendar below for the most up-to-date information.
Grading
There will be no tests, midterms or a final for this course. Your grade will depend on:
1) your active participation in class during practice sessions, discussions on an assigned research topic, and completing surveys;
2) your general understanding of the material, which will be evident during practice sessions.
The last two classes will include a test practice session covering all semester material, which will give each of you a chance of demostrating your knowledge, especially on the topics you struggled with before. See more on Practice website.
Practice Problems
There will be weekly practice problems assignments, posted here.
You are expected to solve (or at least seriously attempt to solve) all
of them, as you might be called to present it. After the practice
class, I strongly suggest you clearly write up solutions to all
problems, as you might need it later.
The purpose of the survey is for you to self-assess your general understanding of the material, and for me to see the progress of the class. If at any point you realize, you need assistance with the material, please do not hesitate to contact me by email, or in person. Surveys will also include questions about course organization, which will give you an opportunity to address any concerns, ask questions, and influence the future of the course.
Completing surveys will count toward your participation in class, and it is a requirement. I will be collecting your names at the end of the survey (basically, by using another survey), but your responses will stay anonymous. The survey will open during Tuesday and Wednesday, so please complete it in time. I will close the survey on Thursday morning to process it, so it could be discussed that day during class.
Research Assignment
Every other week there will be a research assignment that is related to
the application of quantum theory to the real world, or the appearance
of quantum theory in the real world. See calendar below for these
assignments.
Please research the topic and be prepared to participate in or lead a short discussion on this topic. You are expected to read at least what is suggested here, but strongly encouraged to read more.
Class Calendar
Abbreviation 'NC' stands for the book by Nielsen and Chuang, and 'W' stands for the book by Wilde
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 10:00-11:30am in M 119Contact
Dr. Anna Vershyninaanna@math.uh.edu
please include “MATH 6395” in the subject so that your email won't be regarded as spam
Text
We will mostly follow two 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 buy either of these books.
Prerequisites
For this course it will be excpected that you know the following material well:-Linear Algebra
-Basics of Probability
-Basics of Functional Analysis
It will not be expected that you know any quantum mechanics, computer science, information theory.
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Course Overview 
There will be a lecture every Thursday. Every Tuesday we will dicuss solutions to some practice problems and research assignments. Your grade will depend on you active participation during dicussions and general understanding of the material at the end of the class.
During the course we aim to cover the following topics:
-Basics of quantum mechanics
-Universal quantum computation
-Quantum teleportation
-Quantum error-correction
-Entropy and quantum information
-Noisy quantum channels
This list is subject to change depending on time constrains etc. Check the calendar below for the most up-to-date information.
Grading
There will be no tests, midterms or a final for this course. Your grade will depend on: 1) your active participation in class during practice sessions, discussions on an assigned research topic, and completing surveys;
2) your general understanding of the material, which will be evident during practice sessions.
The last two classes will include a test practice session covering all semester material, which will give each of you a chance of demostrating your knowledge, especially on the topics you struggled with before. See more on Practice website.
Practice Problems 
There will be weekly practice problems assignments, posted here.
You are expected to solve (or at least seriously attempt to solve) all
of them, as you might be called to present it. After the practice
class, I strongly suggest you clearly write up solutions to all
problems, as you might need it later.Surveys
I will be sending a survey every week on Tuesdays, after the practice session. Before taking the survey, please review all material discussed in practice session and make sure you understand it. While taking the survey, please do not use any help (notes, books, internet,...). The survey will be anonymous.
The purpose of the survey is for you to self-assess your general understanding of the material, and for me to see the progress of the class. If at any point you realize, you need assistance with the material, please do not hesitate to contact me by email, or in person. Surveys will also include questions about course organization, which will give you an opportunity to address any concerns, ask questions, and influence the future of the course.
Completing surveys will count toward your participation in class, and it is a requirement. I will be collecting your names at the end of the survey (basically, by using another survey), but your responses will stay anonymous. The survey will open during Tuesday and Wednesday, so please complete it in time. I will close the survey on Thursday morning to process it, so it could be discussed that day during class.
Research Assignment 
Every other week there will be a research assignment that is related to
the application of quantum theory to the real world, or the appearance
of quantum theory in the real world. See calendar below for these
assignments. Please research the topic and be prepared to participate in or lead a short discussion on this topic. You are expected to read at least what is suggested here, but strongly encouraged to read more.
| Date |
Topic |
Reading |
| Sep 11 |
Quantum computers. Who has the biggest and what kind? |
Research devices by: IBM, Intel, Google, D-Wave. Answer: how many qubits, what kind, what are the challenges and advantages Review paper (optional) |
| Sep 25 |
Applications of quantum computers. What problems can they solve? |
D-Wave, Microsoft, find at least one other reference (research at least two applications) Review paper 1 (optional) Review paper 2 (optional) |
| Oct 9 |
Imperfect quantum cloning. Does it imply imperfect FTL communication? |
paper 1 + paper 2 |
| Oct 23 |
Problem of Time |
Wiki + paper 1 (p. 1-3)+ paper 2 (ch. 1-3) |
| Nov 6 |
Black hole paradox | Wiki + paper (lecture 6) |
| Nov 20 |
(Potential) Applications of quantum technology. Atomic clocks, quantum biology, quantum sensors, lasers, GPS, quantum gravity... |
q. biology + quantum Bitcoin mining + graviton+ find at least one other application (research at least two applications from different areas) |
| Nov 29 |
Quantum mechanics in popular culture. What does it get wrong? |
Watch
some movies and/or TV-series, and find at least two occasions, where
quantum mechanics was mentioned or used incorrectly. (Yes, it is your
homework to watch movies!) Ant-man, Thor and Captain America, Interstellar |
Class Calendar
Abbreviation 'NC' stands for the book by Nielsen and Chuang, and 'W' stands for the book by Wilde| Aug 21 Introduction  |
Aug 23 Postulates, Noiseless QT NC 2.2, W 3 |
Aug 28 Practice |
Aug 30 Quantum Gates NC 4.1-4.3 |
| Sep 4 Practice |
Sep 6 Universal Quantum Gates NC 4.4-4.5.1 |
Sep 11 Practice Discussion: Quantum computers. Video: Quantum computing overview |
Sep 13 Universal Quantum Gates+ Noisy QT NC 4.5.2+ NC 2.4, W 4.1-4.3 |
| Sep 18 Practice |
Sep 20 Quantum Noisy Channels NC 8.1-8.3, W 4.4-4.7 |
Sep 25 Practice: Discussion: Applications of quantum computers. |
Sep 27 Schwartz Decomposition+Purification NC 2.5, W 5 |
| Oct 2 Practice 
|
Oct 4 Quantum Protocols NC 2.3, 1.3.7 W 6 |
Oct 9 Practice IBM Q-Experience Discussion: Imperfect quantum cloning. |
Oct 11 Distance Measures NC 9, W 9 |
| Oct 16 Practice |
Oct 18 Quantum Entropy NC 11, W 11 |
Oct 23 Practice Discussion: "Problem of Time" |
Oct 25 Class canceled 
|
| Oct 30 Practice Game: Quantum Tic-Tac-Toe |
Nov 1 Quantum Error Correction NC 10.1-10.3.0 |
Nov 6 Practice Discussion: Black hole paradox. |
Nov 8 Quantum Error Correction NC 10.3.3-10.3.4, 10.5.1, 10.5.5 |
| Nov 13 Practice |
Nov 15 Quantum Error Correction NC 10.5.5-10.5.6 + Overview of the class |
Nov 20 Overview of the class Discussion: Applications of quantum technology. |
Nov 22 Thanksgiving - no class  |
| Nov 27 Test Practice 1 Video: Bird navigation |
Nov 29 Test Practice 2 Discussion: Quantum mechanics in popular culture. |
Congratulations!
 |
Winter break!!!...
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