A subexponential-time quantum algorithm for the dihedral hidden subgroup problem

Details A subexponential-time quantum algorithm for the dihedral hidden subgroup problem A subexponential-time quantum algorithm for the dihedral hidden subgroup problem

2003-02-14

arxiv.org/abs/quant-ph/0302112v2

Physics

Quantum Physics

11 pages. Revised in response to referee reports. Early sections are more accessible; expanded section on other hidden subgrou

Scientific paper

We present a quantum algorithm for the dihedral hidden subgroup problem with time and query complexity $O(\exp(C\sqrt{\log N}))$. In this problem an oracle computes a function $f$ on the dihedral group $D_N$ which is invariant under a hidden reflection in $D_N$. By contrast the classical query complexity of DHSP is $O(\sqrt{N})$. The algorithm also applies to the hidden shift problem for an arbitrary finitely generated abelian group. The algorithm begins with the quantum character transform on the group, just as for other hidden subgroup problems. Then it tensors irreducible representations of $D_N$ and extracts summands to obtain target representations. Finally, state tomography on the target representations reveals the hidden subgroup.

Affiliated with

Also associated with

No associations

Rating

A subexponential-time quantum algorithm for the dihedral hidden subgroup problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A subexponential-time quantum algorithm for the dihedral hidden subgroup problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A subexponential-time quantum algorithm for the dihedral hidden subgroup problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-267654