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Quantum Science and Technology

Accuracy-cost trade-offs for reference VQE calculations of H 2 on IBM quantum hardware

Julen Larrucea, Marita Oliv, Jeanette Miriam Lorenz

Published Oct 15, 2026• 0 citations
Publisher

Abstract

Abstract Variational quantum eigensolver calculations are widely used as reference workflows for assessing near-term quantum hardware, but practical guidance on their accuracy, runtime, and billed usage remains limited. Here, 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 2025–2026. Using a standardized Qiskit Nature workflow, we benchmark the impact of shot count, backend choice, fermion-to-qubit mapping, optimizer behavior, resilience level, and execution mode on the achievable energy accuracy relative to exact diagonalization. For the H 2 /STO–3G configurations examined, circuit simplification through tapered mappings provides the most consistent accuracy gains, resilience level 1 improves accuracy at a substantial billed-usage premium, and session-based execution yields no systematic accuracy advantage over single-job execution despite markedly higher billed time. The dataset and analysis provide a transparent baseline for assessing current IBM Quantum hardware for quantum-chemistry applications and for estimating the runtime effort and billed usage that non-specialist users can expect from standard workflows.

DOI
10.1088/2058-9565/aeb4e8

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Abstract Variational quantum eigensolver calculations are widely used as reference workflows for assessing near-term quantum hardware, but practical guidance on their accuracy, runtime, and billed usage remains limited. Here, 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 2025–2026. Using a standardized Qiskit Nature workflow, we benchmark the impact of shot count, backend choice, fermion-to-qubit mapping, optimizer behavior, resilience level, and execution mode on the achievable energy accuracy relative to exact diagonalization. For the H 2 /STO–3G configurations examined, circuit simplification through tapered mappings provides the most consistent accuracy gains, resilience level 1 improves accuracy at a substantial billed-usage premium, and session-based execution yields no systematic accuracy advantage over single-job execution despite markedly higher billed time. The dataset and analysis provide a transparent baseline for assessing current IBM Quantum hardware for quantum-chemistry applications and for estimating the runtime effort and billed usage that non-specialist users can expect from standard workflows.
Accuracy-Cost Trade-offs for Reference VQE Calculations of H2_22​ on IBM Quantum Hardware
We present a hardware-validated reference dataset for variational ground-state energy calculations of the hydrogen molecule H2_22​ 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.
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 well known 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 an assessment of current quantum algorithms for molecular modeling on real quantum hardware, highlighting the impact of noise and hardware limitations on the achievable accuracy.
molecule, emphasizing practical implementation and performance on current quantum hardware. Our research presents a comparative study of HEA and UCCSD ansätze on noiseless and noisy simulations and implements VQE on recent IBM quantum computer noise models and a real quantum computer, IBM Fez, providing a fully functional code employing Qiskit 1.2. Our experiments confirm UCCSD's reliability in ideal conditions, while the HEA demonstrates greater robustness to hardware noise, achieving chemical accuracy on state-vector simulation (SVS). The results reveal that achieving ground-state energy within chemical accuracy is feasible without error mitigation during VQE convergence. We demonstrate that current quantum devices effectively optimize circuit parameters despite misestimating simulated energies. The SVS-evaluated energies provide a more accurate representation of the solution quality compared to QPU-estimated energy values, indicating that VQE converges to the correct ground state despite quantum noise. Our study also applies noise mitigation as a postprocessing technique, using zero-noise extrapolation (ZNE) on a real quantum computer. The detailed methodologies presented in this study, including Hamiltonian construction and Fermionic-to-qubit transformations, facilitate flexible adaptation of the VQE approach for various algorithm variants and across different levels of algorithmic implementation.
Abstract Quantum computers are expected to be highly beneficial for chemistry simulations, promising significant improvements in accuracy and speed. The most prominent algorithm for chemistry simulations on NISQ devices is the Variational Quantum Eigensolver (VQE). It is a hybrid quantum-classical algorithm which calculates the ground state energy of a Hamiltonian based on parametrized quantum circuits, while a classical optimizer is used to find optimal parameter values. However, quantum hardware is affected by noise, and it needs to be understood to which extent it can degrade the performance of the VQE algorithm. In this paper, we study the impact of noise on the example of the hydrogen molecule. First, we compare the VQE performance for a set of various optimizers, from which we find NFT to be the most suitable one. Next, we quantify the effect of different noise sources by systematically increasing their strength. The noise intensity is varied around values common to superconducting devices of IBM Q, and curve fitting is used to model the relationship between the obtained energy values and the noise magnitude. Since the amount of noise in a circuit highly depends on its architecture, we perform our studies for different ansatzes, including both hardware-efficient and chemistry-inspired ones. Finally, we compare our results from noisy simulations with experiments on different IBM hardware devices.
Abstract We present a comprehensive quantum chemical study of nine molecules H₂, HeH⁺, LiH, BeH₂, H₂O, NH₃, CH₄, CO₂, and N₂ using the Variational Quantum Eigensolver (VQE) algorithm implemented in Qiskit 2.4.1. Molecular Hamiltonians are constructed in the STO-3G minimal basis set, transformed to qubit operators via the Jordan-Wigner mapping, and optimized using the n-local hardware-efficient ansatz with the SLSQP optimizer. Ground state energies are benchmarked against Full Configuration Interaction (FCI)/STO-3G reference values from authoritative literature sources. VQE achieves accuracies from 96.46% (HeH⁺) to 99.99% (H₂), average 98.68%. Potential energy surfaces are generated for all nine molecules and compared with high level ab initio literature PES references including the Kolos-Wolniewicz H₂ curve, the Polyansky water surface, and the Bytautas-Ruedenberg N₂ FCI surface. Equilibrium bond lengths agree with experiment to within 0.000–0.006 Å. Quantum ansatz circuits are analyzed in detail for all molecules. These results confirm the viability of near-term VQE algorithms for molecular quantum chemistry across diverse bond types and geometries.
Accurate determination of ground-state energies for molecules remains a challenge in quantum chemistry and a cornerstone for progress in fields such as drug discovery and materials design. The Variational Quantum Eigensolver (VQE) represents a leading hybrid quantum-classical paradigm for addressing this challenge; however, its widespread realization is limited by noise and the restricted scalability of current quantum hardware. Achieving efficient simulations on Noisy Intermediate-Scale Quantum (NISQ) devices and forthcoming Fault-Tolerant Application-Scalable Quantum (FASQ) systems demands a detailed understanding of how computational resources scale with molecular complexity and fermion-to-qubit encodings. In this study, resource requirements for VQE implementations employing the Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz are systematically analyzed. The molecular Hamiltonian is formulated in second quantization and mapped to qubit operators through the Jordan-Wigner (JW), Bravyi-Kitaev (BK), and Parity (Pa) transformations. Hamiltonian reduction strategies, including Z2\mathbb{Z}_2Z2​ tapering and frozen-core approximations, are examined to assess their effect on quantum resource scaling. The analysis reveals that appropriate transformations, when combined with symmetry-based reductions, can substantially reduce qubit counts by up to ≈50%\approx 50\%≈50% and quantum gate counts by up to ≈27.5×\approx 27.5\times≈27.5× and Hamiltonian Pauli string counts by up to ≈2.75×\approx 2.75\times≈2.75×, relative to the corresponding unreduced Hamiltonian representations within the same active-space configuration for the representative set of molecular systems under study. These findings provide practical circuit-level insights for executing chemically relevant simulations on NISQ hardware, while establishing physical-resource baselines that may inform future logical-level analyses targeting FASQ systems.