Academic Bulletin Description: Fundamentals of quantum information processing, including quantum computation, quantum algorithms, quantum cryptography, and basic quantum information theory. Topics include: the quantum circuit model, alternative models, qubits, unitary operators, measurement, entanglement, quantum algorithms for factoring and search, quantum cryptographic key distribution, simulation of physical systems, error-correction and fault-tolerance, quantum channels, complexity of quantum computation, near-term implementations, quantum computer programming.
Full Course Description: This course teaches the fundamentals of quantum information processing, including quantum computation, quantum cryptography, and basic quantum information theory. The last 20 years have seen the discovery of algorithms that directly harness the laws of quantum mechanics to speed up certain computations and ensure secrecy of communications. There are fast quantum algorithms to factor large integers and compute discrete logarithms, which, if implemented, threaten the security of the encryption schemes in common use today. This possibility has spurred several major and ongoing attempts to build quantum computers, and several companies have announced working (although quite limited) quantum computing devices. Quantum computation might also be useful in simulating complex quantum systems such as large molecules.
We will cover the fundamentals of quantum information processing, both theory and practice, including a programming project.
Credit hours: 3.
Cross-listings: This course is cross-listed with MATH 763 and PHYS 743.
Prerequisites: C or better in any of MATH 344 or MATH 544 or MATH 700, or the equivalent, or permission of the instructor
You should be familiar with calculus (MATH 241) and especially linear algebra (MATH 344 or 544, for example), and know some probability and discrete math. Knowledge of quantum mechanics is NOT a prerequisite; quantum concepts will be introduced as needed. Similarly, knowledge of algorithms and complexity are not prerequisites either; these also will be introduced as needed. (See also Concepts and Buzzwords, below.)
By the end of this course, you should be able to
There will be two 75-minute lectures per week, which constitutes 100% of the course delivery. There will be no separate labs, and there are no plans for distance learning.
There will be regular homework assignments consisting of weekly or biweekly problem sets, to be handed in hardcopy. There will be one midterm exam and one final exam.
There is no formal attendance policy, and attendance will not be taken in lecture. However, you are responsible for knowing anything said in lecture (including timely announcements).
No make-up exams will be given except under emergency circumstances with as much prior notice as possible.
| Coursework | Fraction of grade |
| Homework assignments | 20% |
| Midterm exam | 30% |
| Programming project | 10% |
| Final exam | 40% |
Letter grades correspond to score percentages as follows:
| A | at least 90 |
| B+ | at least 86 and less than 90 |
| B | at least 80 and less than 86 |
| C+ | at least 76 and less than 80 |
| C | at least 70 and less than 76 |
| D+ | at least 66 and less than 70 |
| D | at least 60 and less than 66 |
| F | less than 60 |
Pass/fail: Students make take this course pass/fail. For them, a pass is equivalent to a letter grade of C or better.
This schedule is subject to some alteration, depending on the pacing of the course and student abilities. Homework problem sets will be due in class one week after they are assigned, and will be returned graded within one week, schedule permitting. There are 28 regular class periods lasting 75 minutes each (including the midterm exam) and a 2.5-hour in-class final exam. A "week" is equivalent to two class periods and so may not always line up with an actual calendar week. The date of the midterm exam, given below, is fixed and not subject to change during the course.
| Week | Topic(s) |
| Week 1 | Basic principles of quantum mechanics (just enough to understand quantum information processing) |
| Week 2 | Basic principles (cont.); Intro to quantum gates and circuits |
| Week 3 | Quantum gates and circuits (cont.): representing a 1-qubit state |
| Week 4 | Classical computation versus quantum computation |
| Week 5 | Basic quantum algorithms: Deutsch-Josza, Simon's problem |
| Week 6 | Quantum Fourier transform; phase estimation |
| Week 7 | Shor's quantum algorithm for factoring |
| Week 8 | Grover's fast quantum search algorithm; midterm exam (75 minutes in class) |
| Week 9 | Quantum cryptography: the BB84 protocol; programming project info |
| Week 10 | Quantum teleportation; dense coding |
| Week 11 | Intro to quantum information: mixed states; properties of quantum channels |
| Week 12 | Quantum error correction |
| Week 13 | Quantum error correction (cont.); fault-tolerance |
| Week 14 | Properties of quantum entanglement: Bell inequalities |
| Week 15 | TBD (overflow?) |
| Week 16 | Overflow, Review |
| Finals | Final exam (2.5 hours): cumulative but emphasizing material since midterm |
As time permits, additional topics may include: physical realizations such as nuclear magnetic resonance; ions in traps; solid state devices; simulation of quantum systems; quantum machine learning.
Reading and lectures: You (the student) are expected to read all assigned material before the lecture begins.
Attendance policy: There is no required attendance policy, but if for some reason you cannot attend class, you are responsible for any material covered during your absence. Late arrivals must enter the classroom quietly and discreetly.
Homework: The homework exercises are chiefly for your own benefit. Homework is graded on a pass/fail basis and only counts for 20% of the grade. You may collaborate and consult outside sources freely when doing the homework, but you must tell me who you are collaborating with and properly cite any external sources that you use. Please remember, however, that the best way to master the material is to try the exercises on your own, then submit your own work to get feedback on it. (You will get credit even if you do not solve the problem, as long as you make an honest effort.) Homework is due in class on the due date, unless otherwise specified. This is a sharp deadline. Homework will be accepted up to 24 hours after the due time with a 20% penalty. (Homework will not be accepted more than 24 hours late.) If you wish, you may submit your homework via email to the instructor or to the TA (if there is one).
Exams: The midterm exam will be given in class and is open-book/open-notes. The final exam will be a take-home exam (open book/open notes/external sources allowed with proper citation (see Academic Honesty, below)). You may use any printed materials you wish during the midterm, but you may not use electronic devices except for use as timepieces or legitimate use by disabled students with prior notice. No make-up exams will be given except under extreme circumstances (such as severe illness or death in the immediate family) in which case you must give me notice well before the exam if at all possible. Final exam submission will be through upload on CSE Dropbox.
General guidelines and resources: You are expected to practice the highest possible standards of academic integrity. Any deviation from this expectation will result in a minimum academic penalty of your failing the assignment, and will result in additional disciplinary measures. This includes improper citation of sources, using another student's work, and any other form of academic misrepresentation. (For class-specific rules, see "Academic honesty policies specific to this course," below.)
The first tenet of the Carolinian Creed is, "I will practice personal and academic integrity."
Below are some websites for you to visit to learn more about University policies:
Academic honesty policies specific to this course: Examination work is expected to be the sole effort of the student submitting the work. Collaboration and reference to outside sources on the homework is allowed, provided all collaborators (whether or not they are students) and outside sources used must be listed at the top of the first page. Every instance of a suspected violation will be reported to the Office of Student Conduct and Academic Integrity. Students found guilty of deliberate or grossly negligent violations of these policies will receive a grade of F for the whole course in addition to whatever disciplinary sanctions are applied by the University. Note that this penalty is much more severe than the minimum penalty described above.
Proper use of computing resources: Students are expected to be aware of the university policy on use of computing resources, including the Student Guidelines for Responsible Computing, as well as the college and departmental policies on proper use of computing resources. Every instance of a suspected violation will be reported.
Students with disabilities should contact the Student Disability
Resource Center. The contact information is below:
1705 College Street, Close-Hipp Suite 102,
Columbia, SC 29208
Phone:803.777.6142 Fax: 803.777.6741
Email: sasds@mailbox.sc.edu
Web:
https://sc.edu/about/offices_and_divisions/student_disability_resource_center/index.php
These services provide assistance with accessibility and other issues to
help those with disabilities be more successful. Additionally, students
should review the information on the Disabilities Services
website and communicate with the professor during the first week of
class. Other academic support resources may help students be more
successful in the course as well.
Library Services
(http://www.sc.edu/study/libraries_and_collections)
Writing Center
(http://www.cas.sc.edu/write)
Carolina Tech Zone (http://www.sc.edu/technology/techstudents.html)
Here are some concepts related to the subject. Some are background (e.g., propositional logic), and you may already know them. Others (e.g., the singular value decomposition of a matrix) I'm guessing you don't know, and so you will learn them in this course. I don't expect any of you to know a significant fraction of the topics on this list. I will cover much of this in class, especially the algebra and computer science. All this material can be found in standard textbooks in the areas given. Much of it can also be found in our textbooks and in the course notes, both in the main part and the appendices.