Topological quantum hashing with the icosahedral group.
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.
Burrello
Michele
M
International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste, Italy.
Xu
Haitan
H
Mussardo
Giuseppe
G
Wan
Xin
X