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 renor- malization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/ε)), we can approximate all SU(2) matrices to an average error ε with a cost of O(log(1/ε)) in time. The algorithm is applicable to generic quantum compiling.

Topological Quantum Hashing with the Icosahedral Group / M., Burrello; H., Xu; Mussardo, Giuseppe; X., Wan. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 104:(2010), pp. 160502-160506. [10.1103/PhysRevLett.104.160502]

Topological Quantum Hashing with the Icosahedral Group

Mussardo, Giuseppe;
2010-01-01

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 renor- malization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/ε)), we can approximate all SU(2) matrices to an average error ε with a cost of O(log(1/ε)) in time. The algorithm is applicable to generic quantum compiling.
2010
104
160502
160506
M., Burrello; H., Xu; Mussardo, Giuseppe; X., Wan
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/17084
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