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Title: Calculation of Molecular Vibrational Spectra on a Quantum Annealer

Abstract

Until recently molecular energy calculations using quantum computing hardware have been limited to gate-based quantum computers. In this paper, a new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer. The key idea of the method is a mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits. The algorithm is general and represents a new revolutionary approach for solving the real symmetric eigenvalue problem on a quantum annealer. The method is applied to two chemically important molecules: O2 (oxygen) and O3 (ozone). The lowest two vibrational states of these molecules are computed using both a hardware quantum annealer and a software based classical annealer. Extension of the algorithm to higher dimensions is explicitly demonstrated for an N-dimensional harmonic oscillator (N ≤ 5). The algorithm scales exponentially with dimensionality if a direct product basis is used but will exhibit polynomial scaling for a nondirect product basis.

Authors:
ORCiD logo [1];  [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
  2. Department of Chemistry, Marquette University, Milwaukee, Wisconsin 53021, United States
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1545969
Alternate Identifier(s):
OSTI ID: 1558208
Report Number(s):
LA-UR-18-29586
Journal ID: ISSN 1549-9618
Grant/Contract Number:  
20170221ER; 89233218CNA000001
Resource Type:
Published Article
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Name: Journal of Chemical Theory and Computation Journal Volume: 15 Journal Issue: 8; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Inorganic and Physical Chemistry; quantum computing; quantum annealing; eigensolver; molecular spectrum; QAE

Citation Formats

Teplukhin, Alexander, Kendrick, Brian K., and Babikov, Dmitri. Calculation of Molecular Vibrational Spectra on a Quantum Annealer. United States: N. p., 2019. Web. doi:10.1021/acs.jctc.9b00402.
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Teplukhin, Alexander, Kendrick, Brian K., & Babikov, Dmitri. Calculation of Molecular Vibrational Spectra on a Quantum Annealer. United States. https://doi.org/10.1021/acs.jctc.9b00402
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Teplukhin, Alexander, Kendrick, Brian K., and Babikov, Dmitri. Wed . "Calculation of Molecular Vibrational Spectra on a Quantum Annealer". United States. https://doi.org/10.1021/acs.jctc.9b00402.
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@article{osti_1545969,
title = {Calculation of Molecular Vibrational Spectra on a Quantum Annealer},
author = {Teplukhin, Alexander and Kendrick, Brian K. and Babikov, Dmitri},
abstractNote = {Until recently molecular energy calculations using quantum computing hardware have been limited to gate-based quantum computers. In this paper, a new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer. The key idea of the method is a mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits. The algorithm is general and represents a new revolutionary approach for solving the real symmetric eigenvalue problem on a quantum annealer. The method is applied to two chemically important molecules: O2 (oxygen) and O3 (ozone). The lowest two vibrational states of these molecules are computed using both a hardware quantum annealer and a software based classical annealer. Extension of the algorithm to higher dimensions is explicitly demonstrated for an N-dimensional harmonic oscillator (N ≤ 5). The algorithm scales exponentially with dimensionality if a direct product basis is used but will exhibit polynomial scaling for a nondirect product basis.},
doi = {10.1021/acs.jctc.9b00402},
journal = {Journal of Chemical Theory and Computation},
number = 8,
volume = 15,
place = {United States},
year = {Wed Jul 17 00:00:00 EDT 2019},
month = {Wed Jul 17 00:00:00 EDT 2019}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1021/acs.jctc.9b00402
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Cited by: 20 works
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Figures / Tables:

Figure 1 Figure 1: Computed wave functions of the ground and first excited states. The molecules are (A) O2 and (B) O3, and the wave function is squared for ozone. Red and green bold curves are the results of a classical numerical eigensolver (LAPACK). Solid thin black curves were obtained using QAEmore » with a software classical QUBO solver (they lie on top of the LAPACK curves). Dashed black curves are the results obtained using QAE with a hardware quantum annealer (DWave machine). The blue curve is (A) oxygen potential V(r) and (B) the minimum energy path V(ρ) for ozone.« less
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