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We improved the variational quantum eigensolver (VQE) for simulating periodic systems. New methods accurately calculate ground and excited state energies for molecules like the hydrogen chain, overcoming previous deviations from exact results.

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Materials science

Background:

  • The variational quantum eigensolver (VQE) is a leading quantum algorithm for molecular simulations on current quantum hardware.
  • Simulating periodic systems, crucial for materials science, presents challenges for standard VQE implementations.
  • Existing VQE methods show significant errors when applied to periodic systems like the 1D hydrogen chain.

Purpose of the Study:

  • To generalize the VQE algorithm for accurate simulation of periodic quantum systems.
  • To address the observed deviations in ground-state energy calculations for periodic systems using VQE.
  • To develop enhanced quantum simulation techniques for electronic structure properties.

Main Methods:

  • Generalizing the variational quantum eigensolver (VQE) for periodic systems.
  • Introducing a modified VQE algorithm with unitary transformation of Hartree-Fock orbitals to simplify wave functions.
  • Combining VQE with the quantum subspace expansion (QSE) approach for improved accuracy.

Main Results:

  • Both proposed schemes, modified VQE and VQE/QSE, accurately describe the potential energy curve of a 1D hydrogen chain.
  • The VQE/QSE approach shows excellent agreement with exact full configuration interaction (FCI) results for excited states.
  • The modified VQE successfully avoids complex wave functions, enhancing simulation stability.

Conclusions:

  • The developed VQE modifications offer accurate quantum simulations for periodic systems.
  • These methods significantly improve upon existing VQE algorithms for electronic structure calculations.
  • The VQE/QSE approach is particularly promising for high-accuracy excited state calculations in periodic materials.