Accuracy-Cost Trade-offs for Reference VQE Calculations of H$_2$ on IBM Quantum Hardware

TL;DR

This paper provides a validated dataset and analysis of variational quantum eigensolver (VQE) calculations for H extsubscript{2} on IBM Quantum hardware, benchmarking accuracy, costs, and hardware choices.

Contribution

It offers a comprehensive, hardware-validated dataset and analysis to benchmark and understand the accuracy-cost trade-offs in quantum chemistry calculations on IBM Quantum devices.

Findings

Circuit simplification via tapered mappings improves accuracy.

Resilience level 1 enhances accuracy but increases costs.

Session-based execution does not improve accuracy despite higher costs.

Abstract

We present a hardware-validated reference dataset for variational ground-state energy calculations of the hydrogen molecule H\(_2\) on several IBM Quantum processors available in 2026. Using a standardized workflow, we benchmark the impact of shot count, backend choice, optimization strategy, and runtime variability on the achievable energy accuracy relative to exact diagonalization. The resulting dataset and analysis provide a transparent baseline for assessing the current capabilities and limitations of IBM Quantum hardware for quantum-chemistry applications, and are meant to ease the entry for new users by providing a comprehensive overview of choices and their effects as well as runtime efforts and costs that can be expected. Across the configurations studied here, circuit simplification through tapered mappings provides the most consistent accuracy gains, resilience level 1 improves accuracy at a substantial cost premium, and session-based execution yields no systematic accuracy advantage over single-job execution despite markedly higher billed time.