BenchQC: A Benchmarking Toolkit for Quantum Computation

The Variational Quantum Eigensolver (VQE) is a promising algorithm for quantum computing applications in chemistry and materials science, particularly in addressing the limitations of classical methods for complex systems. This study benchmarks the performance of the VQE for calculating ground-state energies of aluminum clusters (Al$^-$, Al$_2$, and Al$_3^-$) 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. Our findings demonstrate that certain optimizers achieve efficient and accurate convergence, while circuit choice and basis set selection significantly impact accuracy, with higher-level basis sets closely matching classical computation data from Numerical Python Solver (NumPy) and Computational Chemistry Comparison and Benchmark DataBase (CCCBDB). To evaluate the workflow under 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 percent. The results establish VQE's capability for reliable energy estimations and highlight the importance of optimizing quantum-DFT parameters to balance computational cost and precision. This work paves the way for broader VQE benchmarking on diverse chemical systems, with plans to make results accessible on Joint Automated Repository for Various Integrated Simulations (JARVIS) and develop a Python package to support the quantum chemistry and materials science communities in advancing quantum-enhanced discovery.