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Discrete wigner function derivation of the Aaronson—Gottesman tableau algorithm.
Kocia, Lucas.
Huang, Yifei.
Love, Peter J.
2017.
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Description
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
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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 SU(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. © 2017 by the authors. Licensee MDPI, Basel, Switzerland.
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Creator department
Tufts University. Department of Physics and Astronomy.
Subject
Quantum computing.
Permanent URL
http://hdl.handle.net/10427/014361
Citation
Kocia, Lucas, Yifei Huang, and Peter Love. "Discrete Wigner Function Derivation of the Aaronson-Gottesman Tableau Algorithm." Entropy 19, no. 7 (July 11, 2017): 353. doi:10.3390/e19070353.
ID:
w0892p305
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