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Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation.

Enhua Xu1, Yuma Shimomoto1, Seiichiro L Ten-No1

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This study introduces a quantum computing approach using many-body expansion (MBE) to calculate molecular energies. The method accurately determines ground and excited states, showing promise for complex chemical systems.

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Electronic Structure Theory

Background:

  • Accurate calculation of molecular electronic structures is crucial for understanding chemical properties and reactions.
  • Existing methods face challenges with strongly correlated systems and computational resource demands.
  • The many-body expansion (MBE) offers a fragment-based approach to simplify complex electronic structure calculations.

Purpose of the Study:

  • To develop and validate a quantum computing-based many-body expansion (MBE) framework for calculating ground and excited state energies.
  • To assess the accuracy and resource efficiency of the proposed MBE method using variational quantum eigensolver and deflation algorithms.
  • To investigate the impact of approximations and noise on the energy calculations for molecular systems.

Main Methods:

  • Utilized the many-body expansion (MBE) to decompose electronic structures into manageable fragments.
  • Employed the variational quantum eigensolver (VQE) and deflation algorithms to solve for fragment energies.
  • Incorporated approximations, such as partial generalization of the unitary coupled cluster singles and doubles (UCCSD) operator, to conserve quantum resources.

Main Results:

  • Successfully calculated ground and excited state energies for molecules including LiH, CH+, and H2O.
  • Investigated potential energy surfaces for bond-breaking in H2O and N2, demonstrating reliable descriptions.
  • Model simulations highlighted the critical importance of precise energy estimation for lower-order MBE fragments, especially concerning shot noise.

Conclusions:

  • The quantum-enhanced MBE approach provides a reliable method for determining molecular energies, including for strongly correlated systems.
  • The proposed approximations effectively conserve quantum resources while maintaining accuracy.
  • Precise energy calculations are essential for the successful application of MBE in quantum chemistry.