Toward a QUBO-Based Density Matrix Electronic Structure Method

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 Schrodinger 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.

Automated summary

Density matrix electronic structure theory is widely used in quantum chemistry to reduce computational cost. In this study, a method to compute the density matrix using a quadratic unconstrained binary optimization (QUBO) solver is proposed and explored. The algorithm's parameters, precision, and efficiency are investigated. The results show that the direct construction of the density matrix using a QUBO formulation is feasible but has room for improvement in terms of efficiency and precision. Alternative methods that could lead to a more efficient QUBO-based density matrix construction are suggested.