Ground States via Spectral Combing on a Quantum Computer

TL;DR

This paper introduces Spectral Combing, a quantum algorithm that efficiently finds ground states of many-body systems without needing a good initial guess, by entangling states and transferring energy through avoided level crossings.

Contribution

It presents a novel spectral combing technique that does not depend on large energy gaps, with explicit quantum gate constructions and classical simulation results showing potential advantages over adiabatic methods.

Findings

Spectral Combing can find ground states without initial overlap.

The method requires fewer gates than Quantum Adiabatic Algorithm in some cases.

Classical simulations demonstrate the algorithm's feasibility on small quantum computers.

Abstract

A new method is proposed for determining the ground state wave function of a quantum many-body system on a quantum computer, without requiring an initial trial wave function that has good overlap with the true ground state. The technique of Spectral Combing involves entangling an arbitrary initial wave function with a set of auxiliary qubits governed by a time dependent Hamiltonian, resonantly transferring energy out of the initial state through a plethora of avoided level crossings into the auxiliary system. The number of avoided level crossings grows exponentially with the number of qubits required to represent the Hamiltonian, so that the efficiency of the algorithm does not rely on any particular energy gap being large. We give an explicit construction of the quantum gates required for the realization of this procedure and explore the results of classical simulations of the algorithm on a small quantum computer with up to 8 qubits. We show that for certain systems and comparable results, Spectral Combing requires fewer quantum gates to realize than the Quantum Adiabatic Algorithm.