Exact distributed quantum algorithm for generalized Simon's problem

TL;DR

This paper introduces an exact distributed quantum algorithm for the generalized Simon's problem, achieving exponential speedup over classical methods and improved practicality over previous quantum algorithms.

Contribution

It characterizes the problem's structure in distributed settings and refines the quantum algorithm to be exact using amplitude amplification, with fewer qubits needed.

Findings

Exponential acceleration over classical algorithms.

Enhanced exactness and generalizability compared to prior quantum algorithms.

Reduced qubit requirements for the oracle in the distributed quantum setting.

Abstract

Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and also a special hidden subgroup problem. In this paper, we present two key contributions. Firstly, we characterize the structure of the generalized Simon's problem in distributed scenario and introduce a corresponding distributed quantum algorithm. Secondly, we refine the algorithm to ensure exactness due to the application of quantum amplitude amplification technique. Our algorithm offers exponential acceleration compared to the distributed classical algorithm. When contrasted with the centralized quantum algorithm for the generalized Simon's problem, our algorithm's oracle requires fewer qubits, thus making it easier to be physically implemented. Particularly, the exact distributed quantum algorithm we develop for the generalized Simon's problem outperforms the best previously proposed distributed quantum algorithm for Simon's problem in terms of generalizability and exactness.