Subject 
A computer is a physical device that helps us process information by executing algorithms. An algorithm is a welldefined procedure, with finite description, for realizing an informationprocessing task. An informationprocessing task can always be translated into a physical task. When designing complex algorithms and protocols for various information processing tasks, it is very helpful, perhaps essential, to work with some idealized computing model. However, when studying the true limitations of a computing device, especially for some practical reason, it is important not to forget the relationship between computing and physics. Real computing devices are embodied in a larger and often richer physical reality than is represented by the idealized computing model. Quantum information processing is the result of using the physical reality that quantum theory tells us about for the purposes of performing tasks that were previously thought impossible or infeasible. Devices that perform quantum in formation processing are known as quantum computers. In this class we examine how quantum computers can be used to solve certain problems more efficiently than can be done with classical computers, and also how this can be done reliably even when there is a possibility for errors to occur.. 
Prerequisites 
Mathematical maturity; APPM 2360, APPM 3310, CSCI 2820,MATH 2130, MATH 2135, or something else covering linear algebra. If you have not taken those classes but believe that your background is close to being sufficient, please make sure you have filled up any potential gaps by the end of the second week of classes. If you are not sure whether your background suffices, please see the instructor. The course is designed for ungraduate students but may be suitable for some graduate students. 
Instructors 
Alexandra Kolla (alexandra.kolla [at] colorado [dot] edu) 122 ECES [AK] Graeme Smith (Graeme.Smith@Colorado.edu)JILA S326 [GS]

Graders 
Computer Science: Steven Kordonowy (Steven.Kordonowy@colorado.edu) Physics: Ariel Shlosberg (Ariel.Shlosberg@Colorado.EDU) Matteo Wilczak(matteo.wilczak@colorado.edu)

Times 
MWF 2:00PM  2:50PM DUAN G130 
Office Hours 
Alexandra Kolla/ Graeme Smith: Friday 3:004:00 pm, JILA X317. Ariel Shlosberg: Tu/Th 2:004:00pm, DUANG2B90 (physics help room) Steven Kordonowy: Th 11am12pm, ECAE 124. Matteo Wilczak: Wednesday, 12pm, DUANG2B90 (physics help room) 
#  Date  Topic  Lecture Slides  Reading Material 

1  M January 13  Introduction to Quantum Computing  Slides  Chapter 1 of textbook 
2  W January 15  Introduction to Quantum Computing, Part II  Slides  Chapter 1 of textbook 
3  F January 17  Introduction to Quantum Computing, Part III  Slides  Chapter 1 of textbook 
4  W January 22  The General Computational Process.  Slides  Chapter 2.1 of textbook 
5  F January 24  Deutsch's Problem.  Slides  Chapter 2.2 of textbook 
6  M January 27  Linear Algebra refresher.  Slides  Appendix A of textbook 
7  W January 29  Linear Algebra refresher.  Slides  Appendix A of textbook 
8  F January 31  Deutsche's Problem, revisited.  Slides  Chapter 2.2 of textbook 
9  M February 3  Bernstein Vazirani.  Slides  Chapter 2.4 of textbook 
10  W February 5  Bernstein Vazirani continued, setup of Simon's Problem.  Slides  Chapters 2.4, 2.5 of textbook 
11  F February 7  Simon's Problem.  Slides  Chapters 2.5 of textbook 
12  M February 10  Simon's Problem.  Slides  Chapters 2.5 of textbook 
13  W February 12  Midterm 1.  
14  F February 14  Quantum Cryptography, BB84.  Slides  Chapters 6.1,6.2 of textbook 
15  M February 17  Quantum Cryptography, BB84 continued.  Slides  Chapters 6.1,6.2 of textbook 
16  W February 19  Quantum Cryptography, BB84 continued.  Slides  Chapters 6.1,6.2 of textbook 
17  F February 21  Quantum Cryptography, Dense Coding.  Slides  Chapters 6.1,6.2,6.4 of textbook 
18  M February 24  Dense Coding.  Slides  Chapter 6.4 of textbook 
19  W February 26  Teleportation.  Slides  Chapter 6.5 of textbook 
20  F February 28  GHZ Puzzle.  Slides  Chapter 6.6 of textbook 
21  M March 2  Period Finding, Shor's Algorithm.  Slides  Chapter 3.4 of textbook 
22  W March 4  Period Finding, Shor's Algorithm.  Slides  Chapter 3.43.7 of textbook 
23  F March 6  Period Finding, Shor's Algorithm.  Slides  Chapter 3.43.7 of textbook 
24  M March 9  Period Finding, Shor's Algorithm.  Slides  Chapter 3.43.7 of textbook 
25  W March 1  Period Finding, Shor's Algorithm, Cryptography introduction.  Slides  Chapter 3.43.7 of textbook 
26  F March 13  NO CLASSREADING MATERIAL ON MODULAR ARITHMETIC.  Chapter 3.43.7 of textbook  
27  M March 30  Grover's Search.  Slides, Video  Chapter 4.1 of textbook 
28  F April 3  Grover's Search, contd.  Slides, Video  Chapter 4 of textbook 
29  M April 6  Grover's Search with reflections.  Slides, Video  Chapter 4 of textbook 
30  W April 8  Grover's Search Optimality.  Slides, Video  Chapter 4 of textbook 
31  F April 10  Grover's Search Optimality, Quantum Complexity.  Slides, Video  Chapter 4 of textbook 
33  M April 13  Quantum Information Theory, Error Correcting Codes.  Slides, Video  Chapter 5 of textbook 
34  W April 15  Quantum Information Theory, Error Correcting Codes.  Slides, Video  Chapter 5 of textbook 
35  F April 17  Quantum Information Theory, Error Correcting Codes.  Slides, Video  Chapter 5 of textbook 
36  M April 20  Quantum Information Theory, Error Correcting Codes.  Slides, Video  Chapter 5 of textbook 
37  W April 22  Quantum Information Theory, Error Correcting Codes.  Slides, Video  Chapter 5 of textbook 
38  F April 24  Quantum Information Theory, Error Correcting Codes.  Slides, Video  Chapter 5 of textbook 
39  M April 27  Classical and Quantum Complexity, Hamiltonians.  Slides, Video 
Homework #  Due  Homework Solutions 

HW0  January 20  Solutions 
HW1  January 27  Solutions 
HW2  February 3  Solutions 
HW3  February 10  Solutions 
Solutions  
HW4  February 24  Solutions 
HW5  March 2  Solutions 
Practice Problems for Midterm 2  Solutions  
Solutions  
Homework 

There will be weekly homework, including Homework 0. 
They have to be turned in individually by each student . 
Please do not forget to cite your sources (you will get a zero if you use material from elsewhere and do not cite the source!) ***Absolutely no late homework accepted***. Instead, the lowest two homework grades will be dropped. 
Exams 

There will be two midterms and a Final exam. More details to come. 
Grading 

30% homeworks, 20% each midterm, and 30% final exam. Extra 2% points may be given for class participation at various occasions. 

Chapter 1: " Classical and Quantum Bits and Circuits " (1 week) 
 We will start with "basic" material about quantum bits, unitary matrices, quantum gates and circuits, and quantum computation. 
Chapter 2: " Simple Quantum Algorithms" (1 week)

 We will cover Simon's, BernsteinVazirani, and Deutsch's algorithms. 
Chapter 6: "Fewqubit Protocols" (about 2 weeks)

 We will cover teleportation, dense coding, quantum cryptography. 
Chapter 4 : "Quantum Search" (1 week)

 We will cover Grover's algorithm. 
Chapter 3 : "Quantum Factoring" (12 weeks)

 We will cover quantum factoring. 
Chapter 5 : "Quantum Error Correction" (remaining time)

 We will cover quantum information theory and error correcting codes. 