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 , we can approximate all SU(2) matrices to an average error with a cost of in time. The algorithm is applicable to generic quantum compiling.
- Received 3 April 2009
DOI:https://doi.org/10.1103/PhysRevLett.104.160502
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