The course I’m teaching next term:
CSE 599 (Special Topics in Computer Science)
Quantum Computing
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Instructor: Dave Bacon
Time: Monday and Friday, 1:30-2:50, Wednesday 1:00-2:20
Location: CSE 503
What are the ultimate limits to the information processing power of computing machines? Since computers are physical devices, it makes sense to look for the answer to this question through the lens of our theories of physics. Astoundingly it was discovered over a decade ago that there exists a completely different kind of a computer than today’s modern computer. This new type of computer has the peculiar feature that it processes information according to the laws of quantum physics. Remarkably, such quantum computers have been shown to possess superior computing power over today’s classical computers. For example, in 1994 Peter Shor showed that a quantum computer could efficiently factor whole numbers (a task for which there is no known efficient classical algorithm.) This discovery is especially important since it tells us that if we build a large scale quantum computer, the most widely used public key cryptosystems will no longer be secure.
This course will serve as an introduction to the theory of quantum information science. Today this field is too large to cover in one course, but we will cover two of the most exciting fields in quantum computing: quantum algorithms and quantum error correction. No prior knowledge of quantum theory is necessary for this course, but prior exposure to linear algebra will be assumed.
The course will run three days a week from Wednesday January 4, to Friday February 17. Questions about the course can be directed to Dave Bacon at dabacon[aaattt]cs.washington.edu .
The course has a number which makes it sound like it is for sale, 599.
Is 599 retail or wholesale? Before or after my student discount? Tax included?
Can we see the syllabus? Where’s the course website?
Are you going to do follow-on courses on quantum computing technologies, then quantum computer architecture? If so, will that make UW the first university with an organized QC curriculum?
I know what groups are but what do you mean by “representation theory of …”
Website and syllabus coming! 599 does not include tax and you must pay in quantum currency.
The course I really want to eventually teach is “representation theory of groups for quantum information science.”
OK, so you’ve got a group G and a vector space V (let’s work over the field of complex numbers.) Then a representation G is a map from the elements of the group to linear transforms on V which is a homomorphism. What does this mean? Suppose f is the mapping from the group to the linear transforms on V (i.e. matrices.) Then this map is a homomorphism if it satisfies the property f(g_1) f(g_2) =f(g_1g_2) for all g_1,g_2 in the group. A trivial example of a representation is the representation which maps all elements of the group to the one by one matrix with entry 1. I.e. f(g)=[1] for all g in the group. Then you can easily see that f(g_1)f(g_2)=[1][1]=[1]=f(g_1g_2). This representation is called the trivial representation. Other reprsentations are not so trivial!
The study of the representation theory of groups is a powerful tool for studying problems with symmetry. And in particular for quantum computers, where you want some structure for the problem you are working on, it is often useful to work with representations of groups.
So Dave, you must really like the Wigner-Ekart theorem 🙂
You might want to check out a book by William Harter on symmetry and spectroscopy. It may be out of print, it definitely goes into topics most books of that ilk do not! It’s a little non-standard notation sometimes, but its quite nice.