#### Document Type

Article

#### Language

eng

#### Publication Date

10-2-2020

#### Publisher

Royal Society of Chemistry

#### Source Publication

Physical Chemistry Chemical Physics

#### Source ISSN

1463-9076

#### Abstract

Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.

#### Recommended Citation

Teplukhin, Alexander; Kendrick, Brian K.; and Babikov, Dmitri, "Solving Complex Eigenvalue Problems on A Quantum Annealer with Applications to Quantum Scattering Resonances" (2020). *Chemistry Faculty Research and Publications*. 1008.

https://epublications.marquette.edu/chem_fac/1008

## Comments

Accepted version.

Physical Chemistry Chemical Physics, Vol. 22 (October 2, 2020): 26136-26144. DOI. © 2020 Royal Society of Chemistry. Used with permission.