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How to efficiently select an arbitrary Clifford group element (2014)

Robert Koenig and John A. Smolin

American Institute of Physics (AIP)

In: Journal of Mathematical Physics

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Publication Date: 2014-12-16

Description: We give an algorithm which produces a unique element of the Clifford group on n qubits ( C n ) from an integer 0 ≤ i 〈 C n (the number of elements in the group). The algorithm involves O ( n 3 ) operations and provides, in addition to a canonical mapping from the integers to group elements g , a factorization of g into a sequence of at most 4 n symplectic transvections. The algorithm can be used to efficiently select random elements of C n which are often useful in quantum information theory and quantum computation. We also give an algorithm for the inverse map, indexing a group element in time O ( n 3 ).

Print ISSN: 0022-2488

Electronic ISSN: 1089-7658

Topics: Mathematics , Physics

Published by American Institute of Physics (AIP)

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