Ground-State Energy Estimation on Current Quantum Hardware through the Variational Quantum Eigensolver: A Practical Study
Abstract
We investigate the variational quantum eigensolver (VQE) for estimating the ground-state energy of the BeH2 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.
Nacer Eddine Belaloui
Ph.D student in Theoretical Physics
PhD student in Theoretical Physics. Working within CQTech on Variational Quantum Algorithms.
Abdellah Tounsi
Ph.D student in Theoretical Physics
PhD student in mathematical physics at LPMPS. Working on topological quantum computing.
R. Abdelmouheymen Khamadja
Graduate Research Assistant | Theoretical Physics Graduate
Theoretical physics graduate working withing CQTech on quantum algorithms and simulation.
Mohamed Messaoud Louamri
Ph.D student in Theoretical Physics
PhD student in Theoretical Physics and member of CQTech working on Quantum Simulation and on Optimization Problems.
Mohamed Taha Rouabah
Associate Professor of Physics
ARISE Fellow, Principal Investigator at Constantine Quantum Technologies, Associate Professor at University of Constantine 1 (Algeria).