Outline for academic bulletin: Fundamentals of quantum information processing, including quantum computation, quantum cryptography, and 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, information capacity of quantum channels, complexity of quantum computation, near-term implementations, quantum supremacy and quantum advantage.
Overview: This course teaches the fundamentals of quantum information processing, including quantum computation, quantum cryptography, and 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.
Prerequisites: There are no formal prerequisites for this course, but you should be familiar with calculus (MATH 241) and especially linear algebra (MATH 526 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% |
Final exam | 50% |
Letter grades correspond to score percentages as follows:
A | 90-100 |
B+ | 86-90 |
B | 80-86 |
C+ | 76-80 |
C | 70-76 |
D+ | 66-70 |
D | 60-66 |
F | 0-60 |
This list 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. The date of the midterm exam is definite.
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. 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: Tests are given in class and are open-book/open-notes. You may use any printed materials you wish during the test, 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.
Academic honesty: Examination work is expected to be the sole effort of the student submitting the work. If a student collaborates with anyone on the homework (whether or not a student), all collaborators must be listed at the top of the first page. Students are expected to follow the Code of Student Academic Responsibility. Every instance of a suspected violation will be reported. Students found guilty of violations of the Code will receive the grade of F for the course in addition to whatever disciplinary sanctions are applied by the University.
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: Any student with a documented disability should contact the Office of Student Disability Services at 803-777-6142 to make arrangements for appropriate accommodations.
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, both in the main part and the appendices.