Quantum algorithm for obtaining the eigenstates of a physical system

TL;DR

This paper introduces a quantum algorithm leveraging resonance phenomena to efficiently find eigenstates and energy spectra of physical systems, potentially surpassing phase estimation in speed.

Contribution

A novel quantum algorithm that uses resonance effects to determine eigenstates and spectra, offering quadratic speedup over existing phase estimation methods.

Findings

The algorithm successfully finds eigenstates given eigenvalues.

It can determine the energy spectrum of a system.

Achieves quadratic speedup over phase estimation.

Abstract

We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a probe qubit coupled to a quantum system, the system exhibits a resonance dynamics when the frequency of the probe qubit matches a transition frequency in the system. Therefore the system can be guided to evolve to the eigenstate with known eigenvalue by inducing resonance between the probe qubit and a designed transition in the system. This algorithm can also be used to obtain the energy spectrum of a physical system and can achieve even a quadratic speedup over the phase estimation algorithm.