Ulm 2004 – scientific programme
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MP: Theoretische und Mathematische Grundlagen der Physik
MP 4: Quanteninformationstheorie
MP 4.2: Fachvortrag
Tuesday, March 16, 2004, 14:25–14:50, H 21
Hidden symmetry detection on a quantum computer — •Ralf Schützhold1,2 and William G. Unruh2 — 1Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden — 2Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
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 some simple examples, 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).