How to efficiently select an arbitrary Clifford group element

Journal Article · Mon Dec 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4903507· OSTI ID:22403066

Koenig, Robert ^[1]; Smolin, John A. ^[2]

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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)

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})

• OSTI ID: 22403066
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CLIFFORD ALGEBRA
FACTORIZATION
MAPPING
QUANTUM COMPUTERS
QUBITS