The monomial representations of the Clifford group

Authors:
D. M. Appleby;Ingemar Bengtsson;Stephen Brierley;Markus Grassl;David Gross;Jan-Åke Larsson
Affiliations:
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada;Stockholms Universitet, Stockholm, Sweden;Department of Mathematics, University of Bristol, Bristol, UK and QuIC, Ecole Polytechnique, Université Libre de Bruxelles, Brussels, Belgium;Centre for Quantum Technologies, National University of Singapore, Singapore;Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland;Institutionen för Systemteknik, Linköpings Universitet, Linköping, Sweden
Venue:
Quantum Information & Computation
Year:
2012

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Abstract

We show that the Clifford group--the normaliser of the Weyl-Heisenberg group--can be represented by monomial phase-permutation matrices if and only if the dimension is a square number. This simplifies expressions for SIC vectors, and has other applications to SICs and to Mutually Unbiased Bases. Exact solutions for SICs in dimension 16 are presented for the first time.