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Alexander Teplukhin1, Brian K Kendrick, Dmitri Babikov

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Summary
This summary is machine-generated.

This study extends quantum annealing for chemistry by enabling complex eigenvalue problems, crucial for quantum scattering resonances. These advancements pave the way for solving complex quantum dynamics on quantum annealers.

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Quantum Dynamics

Background:

  • Quantum computing offers a novel approach to complex chemistry problems.
  • The Quantum Annealer Eigensolver (QAE) was previously developed for real symmetric matrices.
  • Many physics and chemistry problems require diagonalization of complex matrices, such as quantum scattering resonances.

Purpose of the Study:

  • Generalize the Quantum Annealer Eigensolver (QAE) to handle complex matrices (Hermitian and symmetric).
  • Apply the generalized QAE to compute quantum scattering resonance states.
  • Benchmark the performance of the complex QAE against classical methods.

Main Methods:

  • Developed generalized QAE for complex Hermitian and complex symmetric matrices.
  • Applied the complex QAE to a 1D model potential for O + O collisions.
  • Utilized both software (classical) and hardware (D-Wave 2000Q) annealers.
  • Benchmarked results against the LAPACK linear algebra library.

Main Results:

  • Successfully computed a quantum scattering resonance state using a generalized QAE on a quantum annealer.
  • Demonstrated the capability of quantum annealers to solve complex eigenvalue problems.
  • Achieved comparable results to classical methods (LAPACK) for the tested problem.

Conclusions:

  • This work presents the first numerical solution of a complex eigenvalue problem on a quantum annealer.
  • It is the first treatment of a quantum scattering resonance on any quantum device.
  • The generalized QAE significantly expands the applicability of quantum annealing in computational chemistry and physics.