TY - JOUR

T1 - Toward a QUBO-Based Density Matrix Electronic Structure Method

AU - Negre, Christian F.A.

AU - Lopez-Bezanilla, Alejandro

AU - Zhang, Yu

AU - Akrobotu, Prosper D.

AU - Mniszewski, Susan M.

AU - Tretiak, Sergei

AU - Dub, Pavel A.

N1 - Funding Information:
Research presented in this article was supported by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory (LANL) under project number 20200056DR. This research was also supported by the U.S. Department of Energy (DOE) National Nuclear Security Administration (NNSA) Advanced Simulation and Computing (ASC) program at LANL. We acknowledge the ASC program for providing the support for accessing D-Wave’s Advantage 4.1 computing resource. LANL is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218NCA000001). Assigned: LA-UR-22-20271
Publisher Copyright:
© 2022 American Chemical Society.

PY - 2022

Y1 - 2022

N2 - Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate"the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more efficient than wave function based methods, significant computational effort is involved. Because the Schrödinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size in mean-field type approaches such as Hartree-Fock and density functional theory and is solved as many times in order to reach charge or field self-consistency. We hereby propose and study a method to compute the density matrix by using a quadratic unconstrained binary optimization (QUBO) solver. This method could be useful to solve the problem with quantum computers and, more specifically, quantum annealers. Our proposed approach is based on a direct construction of the density matrix using a QUBO eigensolver. We explore the main parameters of the algorithm focusing on precision and efficiency. We show that, while direct construction of the density matrix using a QUBO formulation is possible, the efficiency and precision have room for improvement. Moreover, calculations performed with quantum annealing on D-Wave's new Advantage quantum computer are compared with results obtained with classical simulated annealing, further highlighting some problems of the proposed method. We also suggest alternative methods that could lead to a more efficient QUBO-based density matrix construction.

AB - Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate"the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more efficient than wave function based methods, significant computational effort is involved. Because the Schrödinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size in mean-field type approaches such as Hartree-Fock and density functional theory and is solved as many times in order to reach charge or field self-consistency. We hereby propose and study a method to compute the density matrix by using a quadratic unconstrained binary optimization (QUBO) solver. This method could be useful to solve the problem with quantum computers and, more specifically, quantum annealers. Our proposed approach is based on a direct construction of the density matrix using a QUBO eigensolver. We explore the main parameters of the algorithm focusing on precision and efficiency. We show that, while direct construction of the density matrix using a QUBO formulation is possible, the efficiency and precision have room for improvement. Moreover, calculations performed with quantum annealing on D-Wave's new Advantage quantum computer are compared with results obtained with classical simulated annealing, further highlighting some problems of the proposed method. We also suggest alternative methods that could lead to a more efficient QUBO-based density matrix construction.

UR - http://www.scopus.com/inward/record.url?scp=85131965444&partnerID=8YFLogxK

U2 - 10.1021/acs.jctc.2c00090

DO - 10.1021/acs.jctc.2c00090

M3 - Article

AN - SCOPUS:85131965444

JO - Journal of Chemical Theory and Computation

JF - Journal of Chemical Theory and Computation

SN - 1549-9618

ER -