A quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

TL;DR

This paper proposes a quantum algorithm that leverages the energy spectrum probing of a quantum system to solve certain discrete mathematical problems efficiently, demonstrating favorable scaling properties.

Contribution

It introduces a novel quantum algorithm based on energy spectrum probing, expanding the toolkit for quantum problem-solving in discrete mathematics.

Findings

Algorithm exhibits favorable scaling for specific problems

Utilizes probe qubit resonance to identify solutions

Applicable within the circuit model of quantum computing

Abstract

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.