Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE

TL;DR

This paper evaluates the current limitations of VQE algorithms on existing quantum hardware for molecular energy estimation, highlighting noise impacts and outlining hardware requirements for future scalability.

Contribution

It introduces optimized strategies for Hamiltonian simplification, ansatz optimization, and classical parameter tuning, applied on IBM quantum hardware for molecular energy calculations.

Findings

Quantum noise significantly hampers accurate energy measurements.

Optimizations reduce circuit depth but do not overcome hardware noise limitations.

Future hardware improvements are necessary for practical quantum chemistry applications.

Abstract

Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides a roadmap for advancing quantum algorithms and hardware toward achieving quantum advantage in molecular modeling.