Scalable, self-verifying variational quantum eigensolver using adiabatic warm starts

TL;DR

This paper introduces an adiabatic approach to the variational quantum eigensolver that iteratively prepares ground states along a Hamiltonian path, with methods to certify accuracy and avoid common optimization issues.

Contribution

It presents a novel adiabatic VQE method with conditions to prevent barren plateaus and local optima, and introduces runtime certification techniques.

Findings

Gradient-based optimization can successfully prepare adiabatic ground states.

Energy-standard-deviation measurements can verify eigenstate accuracy.

The method avoids barren plateau problems and local optima.

Abstract

We study an adiabatic variant of the variational quantum eigensolver (VQE) in which VQE is performed iteratively for a sequence of Hamiltonians along an adiabatic path. We derive the conditions under which gradient-based optimization successfully prepares the adiabatic ground states. These conditions show that the barren plateau problem and local optima can be avoided. Additionally, we propose using energy-standard-deviation measurements at runtime to certify eigenstate accuracy and verify convergence to the global optimum.