Accelerated variational algorithms for digital quantum simulation of many-body ground states

TL;DR

This paper compares adiabatic and variational quantum algorithms for finding many-body ground states, showing variational methods are more resource-efficient but need faster classical optimization, which is improved with new initialization strategies.

Contribution

The paper provides a quantitative comparison of adiabatic and variational methods and introduces two approaches to accelerate classical optimization in variational quantum algorithms.

Findings

Variational methods require fewer quantum resources than adiabatic methods.

New initialization strategies significantly speed up classical optimization convergence.

Variational algorithms are more practical for digital quantum simulators of many-body ground states.

Abstract

One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we first provide a quantitative comparison between the adiabatic and variational methods with respect to required quantum resources on digital quantum simulators, namely the depth of the circuit and the number of two-qubit quantum gates. Our results show that the variational methods are less demanding with respect to these resources. However, they need to be hybridized with a classical optimization which can converge slowly. Therefore, as the second result of the paper, we provide two different approaches for speeding the convergence of the classical optimizer by taking a good initial guess for the parameters of the variational circuit. We show that these approaches are applicable to a wide range of Hamiltonian and provide significant improvement in the optimization procedure.