Noise thresholds for higher-dimensional systems using the discrete Wigner function

Journal Article · Tue Mar 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.032310· OSTI ID:21537405

Dam, Wim van; Howard, Mark ^[1]

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1. Department of Computer Science and Department of Physics, University of California, Santa Barbara, California 93106 (United States)

For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect, and we allow access to imperfect nonstabilizer states or operations. If the noise rate affecting the nonstabilizer resource is sufficiently high, then these states and operations can become simulable in the sense of the Gottesman-Knill theorem, reducing the overall power of the circuit to no better than classical. In this paper we find the depolarizing noise rate at which this happens and consequently the most robust nonstabilizer states and non-Clifford gates. In doing so, we make use of the discrete Wigner function and derive facets of the so-called qudit Clifford polytope, i.e., the inequalities defining the convex hull of all qudit Clifford gates. Our results for robust states are provably optimal. For robust gates we find a critical noise rate that, as dimension increases, rapidly approaches the the theoretical optimum of 100%. Some connections with the question of qudit magic state distillation are discussed.

• OSTI ID: 21537405
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTERS
DEPOLARIZATION
QUANTUM COMPUTERS
QUANTUM STATES
WIGNER THEORY