Quantum hashing with the icosahedral group
Quantum Physics
2015-03-13 v2 Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
High Energy Physics - Theory
Abstract
We study an efficient algorithm to hash any single qubit gate (or unitary matrix) 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 pseudo-groups. 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[log(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.
Cite
@article{arxiv.0903.1497,
title = {Quantum hashing with the icosahedral group},
author = {Michele Burrello and Haitan Xu and Giuseppe Mussardo and Xin Wan},
journal= {arXiv preprint arXiv:0903.1497},
year = {2015}
}
Comments
5 pages, 4 figures; revised version, to appear in Phys. Rev. Lett.