BenchQC: A Benchmarking Toolkit for Quantum Computation

The Variational Quantum Eigensolver (VQE) is a widely studied hybrid classical-quantum algorithm for approximating ground-state energies in molecular and materials systems. This study benchmarks the performance of the VQE for calculating ground-state energies of small aluminum clusters ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mtext>Al</mml:mtext> <mml:msup><mml:mrow></mml:mrow> <mml:mrow><mml:mo>-</mml:mo></mml:mrow> </mml:msup> </mml:mrow> <mml:annotation>$$ {\mathrm{Al}}^{-} $$</mml:annotation></mml:semantics> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mtext>Al</mml:mtext> <mml:msub><mml:mrow></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\mathrm{Al}}_2 $$</mml:annotation></mml:semantics> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mtext>Al</mml:mtext> <mml:msubsup><mml:mrow></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> <mml:mrow><mml:mo>-</mml:mo></mml:mrow> </mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{Al}}_3^{-} $$</mml:annotation></mml:semantics> </mml:math> ) within a quantum-density functional theory (DFT) embedding framework, systematically varying key parameters: (I) classical optimizers, (II) circuit types, (III) number of repetitions, (IV) simulator types, (V) basis sets, and (VI) noise models. All calculations were performed using quantum simulators to evaluate VQE performance under both idealized and noise-augmented conditions. Our findings demonstrate that certain optimizers converge efficiently, while circuit choice and basis set selection have a marked impact on energy estimates, with higher-level basis sets closely matching classical computation data from Numerical Python Solver (NumPy) and Computational Chemistry Comparison and Benchmark DataBase (CCCBDB). To approximate realistic conditions, we employed IBM noise models to simulate the effects of hardware noise. The results showed close agreement with CCCBDB benchmarks, with percent errors consistently below 0.2%. The results demonstrate that VQE can approximate energy estimates under simulated conditions for small aluminum clusters and highlight the importance of optimizing quantum-DFT parameters to balance computational cost and precision. This work contributes to ongoing efforts to benchmark VQE in practical settings and lays the groundwork for future benchmarking tools for quantum chemistry and materials applications.