Addressing hard classical problems with Adiabatically Assisted Variational Quantum Eigensolvers

TL;DR

This paper introduces a hybrid classical-quantum algorithm called AAVQE that enhances variational quantum eigensolvers by adiabatically changing the Hamiltonian, improving convergence on complex problems.

Contribution

The paper proposes a novel AAVQE algorithm that combines adiabatic evolution with VQE to address small gradient issues and improve performance on current quantum hardware.

Findings

Fast convergence on quantum Hamiltonians

Effective in solving hard classical problems

Maintains quantum state close to optimal path

Abstract

We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for this new algorithm is to circumvent the problem of facing very small gradients in the classical optimization piece of a VQE, while being able to run in current hardware efficient devices. A discrete concatenation of VQEs adapted to interpolating Hamiltonians provides a method to keep the quantum state always close to a path faithfully directed to find the final solution. We benchmark this Adiabatically Assisted Variational Quantum Eigensolver (AAVQE) on quantum Hamiltonians and hard classical problems, for which our approach shows fast convergence.