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). PACS: 03.67.Lx, 89.70.+c.