Twenty years after the discovery of Shor's factoring algorithm, I'll survey what we now understand about the structure of problems that admit quantum speedups. I'll start with the basics, discussing the hidden subgroup, amplitude amplification, adiabatic, and linear systems paradigms for quantum algorithms. Then I'll move on to some general results, obtained by Andris Ambainis and myself over the last few years, about quantum speedups in the black-box model. These results include the impossibility of a superpolynomial quantum speedup for any problem with permutation symmetry, and the largest possible separation between classical and quantum query complexities for any problem.
Held Tuesdays at 4:15 pm, in the William R. Hewlett Teaching Center, room 200 (see map). Refreshments in the lobby of Varian Physics at 4:00 pm.
Autumn 2014/15, Committee: A. Linde (Chair), L. Hollberg, B. Macintosh & Young Lee