Discrete Wigner functions and quantum computational speedup

Journal Article · Fri Apr 01 00:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.042302· OSTI ID:20653259

Galvao, Ernesto F ^[1]

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1. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5 (Canada)

Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize the set C{sub d} of states having non-negative W simultaneously in all definitions of W in this class. For d{<=}5 I show C{sub d} is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.

• OSTI ID: 20653259
• Journal Information: Physical Review. A, Vol. 71, Issue 4; Other Information: DOI: 10.1103/PhysRevA.71.042302; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ENERGY LEVELS
FUNCTIONAL ANALYSIS
HILBERT SPACE
INFORMATION THEORY
QUANTUM MECHANICS
QUANTUM NUMBERS
WIGNER DISTRIBUTION