Quantum algorithm for obtaining the energy spectrum of a physical system

TL;DR

This paper introduces a polynomial-time quantum algorithm capable of efficiently determining the energy spectrum of a physical system and preparing energy eigenstates, demonstrated through simulation of the water molecule.

Contribution

A novel quantum algorithm that efficiently extracts the energy spectrum and eigenstates of a system with polynomially many levels, improving upon classical methods.

Findings

Successfully simulated the water molecule's energy spectrum.

The algorithm can deterministically prepare energy eigenstates.

It operates efficiently for systems with polynomially increasing energy levels.

Abstract

We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a polynomially increasing number of energy levels. A probe qubit is coupled to a quantum register that represents the system of interest such that the probe exhibits a dynamical response only when it is resonant with a transition in the system. By varying the probe's frequency and the system-probe coupling operator, any desired part of the energy spectrum can be obtained. The algorithm can also be used to deterministically prepare any energy eigenstate. As an example, we have simulated running the algorithm and obtained the energy spectrum of the water molecule.