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Title: How to efficiently select an arbitrary Clifford group element

We give an algorithm which produces a unique element of the Clifford group on n qubits (C{sub n}) from an integer 0≤i<|C{sub n}| (the number of elements in the group). The algorithm involves O(n{sup 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 4n symplectic transvections. The algorithm can be used to efficiently select random elements of C{sub 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{sup 3})
Authors:
 [1] ;  [2]
  1. Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
  2. IBM T.J. Watson Research Center, Yorktown Heights, New York 10598 (United States)
Publication Date:
OSTI Identifier:
22403066
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CLIFFORD ALGEBRA; FACTORIZATION; MAPPING; QUANTUM COMPUTERS; QUBITS