Randomness: From Doped Semiconductors to Topological Quantum Computing
Speaker: Prof. Xin Wan, Zhejiang University
Series: Topical Seminars
Location: Engineering Quadrangle B205
Date/Time: Tuesday, July 10, 2012, 4:00 p.m. - 5:00 p.m.
Recent experiments on topological states of matter have been accumulating evidence for the existence of exotic quasiparticles that obey non-Abelian statistics, and can be used for topological quantum computation. In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional spacetime form quantum gates, which can be represented by unitary matrices acting in the space of degenerate quasiparticle states. In this talk, I will focus on the algorithms searching for the best braid sequence for a given target quantum gate in the Fibonacci anyon model. I will take an unusual angle and draw analogies between the distribution of braid representations in the space of unitary matrices and that of the impurities in doped semiconductors in the discussion. Such distributions are known to be broad on a logarithmic scale, so the mean values of the distributions are drastically different from the most probable values. This leads to a renormalization group like scheme to compile a desired gate into a braid sequence. Interestingly, in the renormalization group like iteration, the accuracy (or inaccuracy) follows the Wigner-Dyson distribution of the eigenvalue spacing in the unitary ensemble in random matrix theory, which allows a quantitative control of the residual error. I will demonstrate that the new algorithm is marginally more efficient than the textbook example of the Solovay-Kitaev algorithm.
Xin Wan, a 2000 Ph.D. from the Electrical Engineering Department at Princeton University, is currently Professor of Physics at Zhejiang University, and the Dan Tsui Fellow at Hong Kong University. He has worked extensively in Disordered Electronic Systems and the Quantum Hall Effect - both Integer and Fractional.