Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups

TL;DR

This paper introduces a class of non-abelian groups where the hidden subgroup problem can be efficiently solved using quantum algorithms, advancing quantum computational capabilities for specific non-abelian structures.

Contribution

The paper identifies a new family of non-abelian groups with polynomial-time quantum solutions for the hidden subgroup problem, expanding the scope of efficient quantum algorithms.

Findings

Efficient quantum algorithms for the hidden subgroup problem on the new group family.

Demonstration of polynomial-time solutions for specific non-abelian groups.

Potential implications for quantum cryptography and complexity theory.

Abstract

We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer.