QUBO-based density matrix electronic structure method

TL;DR

This paper explores a novel approach to compute the density matrix in quantum chemistry using QUBO solvers, aiming to leverage quantum annealing, but finds current methods need improvements in efficiency and precision.

Contribution

It introduces a QUBO-based method for density matrix computation and compares quantum annealing with classical simulated annealing, highlighting current limitations and potential improvements.

Findings

QUBO formulation enables direct density matrix construction

Quantum annealing shows promise but has efficiency and precision issues

Alternative methods may improve performance in density matrix calculations

Abstract

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 functions based methods, yet significant computational effort is involved. Since the Schr\"odinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size, 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. The method hereby proposed 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 performing Quantum Annealing with the D-Wave's new Advantage quantum processing units is compared with classical Simulated annealing, further highlighting some problems of the proposed method. We also show some alternative methods that could lead to a better performance of the density matrix construction.