2003/04/12 by R. Schützhold, W. G. Unruh, Schützhold, R. +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0304090
8 pages
arxiv created 2006/06/19 · arxiv updated 2009/12/01
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). PACS: 03.67.Lx, 89.70.+c.