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Ground-State Energy Estimation on Current Quantum Hardware through the Variational Quantum Eigensolver: A Practical

Nacer Eddine Belaloui1,2, Abdellah Tounsi1,2, Abdelmouheymen Rabah Khamadja1,2

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This study explores the Variational Quantum Eigensolver (VQE) for molecular ground-state energy estimation. The Heuristic Ansatz (HEA) shows better noise resilience than UCCSD on quantum hardware.

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Quantum algorithms

Background:

  • Accurate estimation of molecular ground-state energies is crucial for chemical simulations.
  • The Variational Quantum Eigensolver (VQE) is a leading quantum algorithm for this task.
  • Assessing VQE performance on current noisy quantum hardware is essential for practical applications.

Purpose of the Study:

  • To investigate the performance of VQE for the BeH2 molecule on real quantum hardware.
  • To compare the efficacy of the Heuristic Ansatz (HEA) and Unitary Coupled Cluster Singles Doubles (UCCSD) ansätze under various noise conditions.
  • To evaluate the feasibility of achieving chemical accuracy without explicit error mitigation during VQE convergence.

Main Methods:

  • Implementation of VQE using Qiskit 1.2 on IBM quantum hardware simulators and a real quantum device (IBM Fez).
  • Comparative analysis of HEA and UCCSD ansätze on noiseless and noisy simulations, including IBM quantum computer noise models.
  • Application of noise mitigation techniques, specifically Zero-Noise Extrapolation (ZNE), as a postprocessing step.
  • Detailed methodologies for Hamiltonian construction and Fermionic-to-qubit transformations.

Main Results:

  • The UCCSD ansatz performs reliably in ideal conditions, while the HEA demonstrates superior robustness against hardware noise.
  • The HEA achieved chemical accuracy on state-vector simulations (SVS).
  • Ground-state energy within chemical accuracy is achievable during VQE convergence even without error mitigation.
  • Quantum devices effectively optimize parameters despite energy misestimations; SVS energies offer a more accurate quality assessment than QPU-estimated energies.

Conclusions:

  • VQE can converge to the correct ground state even in the presence of quantum noise.
  • The HEA is a promising ansatz for noisy quantum computation in quantum chemistry.
  • The study provides a practical framework and validated methodologies for adapting VQE for diverse quantum computing applications.