Official Course site:
https://gauchospace.ucsb.edu/courses/course/view.php?id=14984
Formalities
Weekly Schedule
Prerequisites
This is a physics graduate course without any formal prerequisites. Read on if you are not a physics gradate student who is contemplating taking this course.
For this course I expect the students to be familiar with the basics of quantum mechanics and to be comfortable with finite dimensional linear algebra. Contact me if you have doubts whether this course is appropriate for you or not.
Summary
This will be a physics graduate course on the theory of quantum information and quantum computing. We will go over the fundamentals of quantum information, after which we will discuss some applications including quantum cryptography, quantum algorithms for factoring, searching, and discrete logarithms, and quantum adiabatic optimization. The last part of the course will be devoted to current developments in the physics of information and this part will be determined by what people are most interested in.
Ambitious List of Topics
Topics single quantum systems: pure quantum states, Von Neumann measurements, finite dimensional Hilbert spaces, L2 norm, inner products, unitary transformations, partial measurements, over-complete measurements, POVMs, superoperators, many-worlds interpretation, mutually unbiased bases, entropic uncertainty relations, SIC-POVMs, Wiesner's 1970 quantum tokens, BB84 protocol, amplitudes vs probabilities, Kocher-Specker theorem
Topics multipartite quantum systems: bipartite quantum systems, tensor products, partial trace, entanglement, quantum teleportation, non locality, Bell inequalities, CHSH, quantum communication complexity, entanglement transformations, quantum information theory, quantum channels
Topics quantum computation: quantum gates, quantum circuits, probabilistic computation, approximate transformations, Deutsch-Jozsa algorithm, black-box query complexity, Simon's algorithm, Shor's algorithm for period finding, computational complexity, modular number theory, RSA, Bach's algorithm for factoring through period finding, Shor's algorithm for factoring, discrete logarithms, Diffie-Hellman key exchange, ElGamal encryption, elliptic curves, Shor's algorithm for discrete logarithms, universal sets of quantum gates, DiVincenzo's criteria, Abelian and non-Abelian Hidden Subgroup Problem, Grover' search algorithm, BBBV lower bound on quantum searching, polynomial method for lower bounds, Quantum computing vs NP-hard problems, power of quantum computation, continuous time quantum algorithms, lower bound on quantum searching in continuous time, quantum adiabatic optimization, strengths and weaknesses of QAO, Hamiltonian complexity, BQP vs PSPACE, QMA