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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Quantum algorithms

Background:

  • Quantum computing shows promise for electronic structure problems.
  • Current quantum approaches primarily focus on molecular energies and first-order derivatives.
  • Calculating second-order energy derivatives for nuclear Hessians is crucial but remains limited.

Purpose of the Study:

  • To present an analytic implementation for computing nuclear Hessians using the variational quantum eigensolver (VQE) framework.
  • To extend quantum computing capabilities to advanced quantum chemical simulations.
  • To assess the quantum measurement cost of these calculations.

Main Methods:

  • Analytic implementation of nuclear Hessians within the VQE framework.
  • Comparison with full configuration interaction (FCI) benchmarks.
  • Assessment of quantum measurement costs and optimization using point group symmetry.

Main Results:

  • Accurate prediction of harmonic vibrational frequencies and normal modes, matching FCI benchmarks.
  • Successful application to systems with orbital degeneracy and weak intermolecular interactions.
  • Demonstrated reduction in measurement cost using point group symmetry without compromising accuracy.

Conclusions:

  • The VQE framework can be extended to compute second-order energy derivatives, enabling accurate vibrational spectra prediction.
  • This advancement supports complex simulations, including noncovalent interactions and transition state identification.
  • Incorporating symmetry offers a practical strategy for efficient quantum chemical calculations.