A Subexponential Time Algorithm for the Dihedral Hidden Subgroup Problem with Polynomial Space

TL;DR

This paper presents a modified quantum algorithm for the dihedral hidden subgroup problem that achieves subexponential runtime with polynomial space, improving upon previous algorithms' space complexity.

Contribution

It introduces a new algorithm that reduces space complexity to polynomial while maintaining subexponential runtime for the dihedral hidden subgroup problem.

Findings

Achieves subexponential time complexity

Reduces space requirement to polynomial

Improves efficiency over previous algorithms

Abstract

In a recent paper, Kuperberg described the first subexponential time algorithm for solving the dihedral hidden subgroup problem. The space requirement of his algorithm is super-polynomial. We describe a modified algorithm whose running time is still subexponential and whose space requirement is only polynomial.