Hidden symmetry detection on a quantum computer

Authors:
R. Schützhold;W. G. Unruh
Affiliations:
Institut für Theoretische Physik, Technische Universität Dresden, Dresden, Germany;Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada and Canadian Institute for Advanced Research Cosmology and Gravity Program
Venue:
Quantum Information & Computation
Year:
2007

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Abstract

The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with f(U[x]) = f(x). Following a discussion regarding which tasks might be solved efficiently by quantum computers, it will be demonstrated by means of a simple example, that the detection of more general hidden (two-point) symmetries V {f(x), f(U[x])} = 0 by a quantum algorithm can also admit an exponential speed-up. E.g., one member of this class of symmetries V {f(x), f(U[x])} = 0 is discrete self-similarity (or discrete scale invariance).