A quantum algorithm for obtaining the energy spectrum of a physical system without guessing its eigenstates

TL;DR

This paper introduces a quantum algorithm that determines the energy spectrum and eigenstates of a physical system without prior knowledge of its eigenstates, using a probe qubit coupled to a quantum register.

Contribution

It presents a novel quantum algorithm that extracts energy spectra without requiring guesswork on eigenstates, enhancing quantum simulation capabilities.

Findings

Successfully identifies energy spectra without eigenstate guesses

Uses a probe qubit to detect resonant transitions

Applicable to general physical systems

Abstract

We present a quantum algorithm that provides a general approach for obtaining the energy spectrum of a physical system without making a guess on its eigenstates. In this algorithm, a probe qubit is coupled to a quantum register $R$ which consists of one ancilla qubit and a $n$-qubit register that represents the system. $R$ is prepared in a general reference state, and a general excitation operator acts on $R$ is constructed. The probe exhibits a dynamical response only when it is resonant with a transition from the reference state to an excited state of $R$ which contains the eigenstates of the system. By varying the probe's frequency, the energy spectrum and the eigenstates of the system can be obtained.