title: Topological quantum hashing with the icosahedral group.
abstract: We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/epsilon)), we can approximate all SU(2) matrices to an average error epsilon with a cost of O(log(1/epsilon)) in time. The algorithm is applicable to generic quantum compiling.
authors.affiliation: International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste, Italy.
authors.forename: Michele
authors.initials: M
authors.lastname: Burrello
authors.forename: Haitan
authors.initials: H
authors.lastname: Xu
authors.forename: Giuseppe
authors.initials: G
authors.lastname: Mussardo
authors.forename: Xin
authors.initials: X
authors.lastname: Wan