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Discrete Wigner Function Derivation of the Aaronson–Gottesman Tableau Algorithm

Department of Physics, Tufts University, Medford, MA 02155, USA
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Entropy 2017, 19(7), 353; https://doi.org/10.3390/e19070353
Received: 3 May 2017 / Revised: 28 June 2017 / Accepted: 4 July 2017 / Published: 11 July 2017
(This article belongs to the Special Issue Quantum Information and Foundations)
The Gottesman–Knill theorem established that stabilizer states and Clifford operations can be efficiently simulated classically. For qudits with odd dimension three and greater, stabilizer states and Clifford operations have been found to correspond to positive discrete Wigner functions and dynamics. We present a discrete Wigner function-based simulation algorithm for odd-d qudits that has the same time and space complexity as the Aaronson–Gottesman algorithm for qubits. We show that the efficiency of both algorithms is due to harmonic evolution in the symplectic structure of discrete phase space. The differences between the Wigner function algorithm for odd-d and the Aaronson–Gottesman algorithm for qubits are likely due only to the fact that the Weyl–Heisenberg group is not in S U ( d ) for d = 2 and that qubits exhibit state-independent contextuality. This may provide a guide for extending the discrete Wigner function approach to qubits. View Full-Text
Keywords: quantum information; quantum computation; semiclassical physics quantum information; quantum computation; semiclassical physics
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Kocia, L.; Huang, Y.; Love, P. Discrete Wigner Function Derivation of the Aaronson–Gottesman Tableau Algorithm. Entropy 2017, 19, 353.

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