Improving the variational quantum eigensolver using variational adiabatic quantum computing

TL;DR

This paper enhances the variational quantum eigensolver (VQE) by integrating variational adiabatic quantum computing (VAQC), which improves initial parameter selection and yields more accurate eigenvalue estimates in quantum chemistry applications.

Contribution

The paper introduces a hybrid quantum-classical homotopy continuation method based on VAQC to improve VQE's convergence and accuracy.

Findings

VAQC provides better initial parameters for VQE.

The combined method achieves more accurate eigenvalues.

Empirical results demonstrate improved performance in quantum chemistry examples.

Abstract

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization problem is in general nonconvex, the method can converge to suboptimal parameter values which do not yield the minimum eigenvalue. In this work, we address this shortcoming by adopting the concept of variational adiabatic quantum computing (VAQC) as a procedure to improve VQE. In VAQC, the ground state of a continuously parameterized Hamiltonian is approximated via a parameterized quantum circuit. We discuss some basic theory of VAQC to motivate the development of a hybrid quantum-classical homotopy continuation method. The proposed method has parallels with a predictor-corrector method for numerical integration of differential equations. While there are theoretical limitations to the procedure, we see in practice that VAQC can successfully find good initial circuit parameters to initialize VQE. We demonstrate this with two examples from quantum chemistry. Through these examples, we provide empirical evidence that VAQC, combined with other techniques (an adaptive termination criteria for the classical optimizer and a variance-based resampling method for the expectation evaluation), can provide more accurate solutions than "plain" VQE, for the same amount of effort.