Toward a QUBO-Based Density Matrix Electronic Structure Method.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Density matrix methods offer computational advantages over wave function methods in electronic structure theory.
• Current mean-field approaches like Hartree-Fock and density functional theory involve cubic scaling computational costs due to solving the Schrödinger equation iteratively.
• Achieving self-consistency in charge or field calculations necessitates repeated eigenvalue problem solutions, increasing computational demand.

Purpose of the Study:

• To propose and investigate a novel method for computing the density matrix using a Quadratic Unconstrained Binary Optimization (QUBO) solver.
• To explore the potential of QUBO-based methods for quantum computing, particularly quantum annealers, in electronic structure calculations.
• To assess the precision and efficiency of a direct density matrix construction approach via QUBO.

Main Methods:

• Direct construction of the density matrix formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem.
• Utilizing a QUBO eigensolver for the density matrix computation.
• Comparing quantum annealing (D-Wave Advantage) results with classical simulated annealing for performance evaluation.

Main Results:

• Demonstrated the feasibility of directly constructing the density matrix using a QUBO formulation.
• Identified that the current QUBO approach has limitations in terms of efficiency and precision.
• Observed discrepancies and challenges when comparing quantum annealing results with classical simulated annealing.

Conclusions:

• The direct QUBO-based density matrix construction is possible but requires significant improvements in efficiency and precision.
• Quantum annealing on the D-Wave Advantage platform presents challenges for this specific QUBO formulation.
• Further research into alternative QUBO-based methods is recommended for more effective density matrix computation.