Variational Quantum Eigensolver: A Comparative Analysis of Classical and Quantum Optimization Methods

TL;DR

This paper compares classical and quantum optimization methods for VQE applied to the Ising model, introduces a new hybrid optimization scheme, and explores optimal quantum circuit structures for NISQ devices.

Contribution

It proposes the QN-SPSA+PSR hybrid optimization method, combining efficiency and accuracy, and analyzes quantum circuit ansatz structures for improved VQE performance.

Findings

QN-SPSA+PSR improves stability and convergence speed.

Potential quantum advantage in VQE optimization routines.

Enhanced strategies for quantum circuit design for NISQ devices.

Abstract

In this study, we study the Variational Quantum Eigensolver (VQE) application for the Ising model as a test bed model, in which we pivotally delved into several optimization methods, both classical and quantum, and analyzed the quantum advantage that each of these methods offered, and then we proposed a new combinatorial optimization scheme, deemed as QN-SPSA+PSR which combines calculating approximately Fubini-study metric (QN-SPSA) and the exact evaluation of gradient by Parameter-Shift Rule (PSR). The QN-SPSA+PSR method integrates the QN-SPSA computational efficiency with the precise gradient computation of the PSR, improving both stability and convergence speed while maintaining low computational consumption. Our results provide a new potential quantum supremacy in the VQAs's optimization subroutine, even in Quantum Machine Learning's optimization section, and enhance viable paths toward efficient quantum simulations on Noisy Intermediate-Scale Quantum Computing (NISQ) devices. Additionally, we also conducted a detailed study of quantum circuit ansatz structures in order to find the one that would work best with the Ising model and NISQ, in which we utilized the properties of the investigated model.