Bridging Quantum Chemistry and MaxCut: Classical Performance Guarantees and Quantum Algorithms for the Hartree-Fock Method

TL;DR

This paper introduces Hartree-Fock-inspired algorithms reformulated as QUBO and MaxCut problems, providing performance guarantees and demonstrating improved stability and potential quantum algorithm applications in quantum chemistry.

Contribution

It develops a novel reformulation of Hartree-Fock SCF algorithms as QUBO and MaxCut problems, enabling performance guarantees and integration with quantum algorithms.

Findings

QUBO-SCF and MaxCut-SCF are more stable than traditional methods.

Demonstrated scalability to systems with up to 220 qubits.

Proposed hybrid quantum-classical algorithms for quantum chemistry.

Abstract

In quantum chemistry, self-consistent field (SCF) algorithms define a nonlinear optimization problem, with both continuous and discrete components. In this work, we derive Hartree-Fock-inspired SCF algorithms that can be exactly written as a sequence of Quadratic Unconstrained Spin/Binary Optimization problems (QUSO/QUBO). We reformulate the optimization problem as a series of MaxCut graph problems, which can be efficiently solved using semi-definite programming techniques. This procedure provides performance guarantees at each SCF step, irrespective of the complexity of the optimization landscape. We numerically demonstrate the QUBO-SCF and MaxCut-SCF methods by studying the hydroxide anion OH- and molecular Nitrogen N2. The largest problem addressed in this study involves a system comprised of 220 qubits (equivalently, spin-orbitals). Our results show that QUBO-SCF and MaxCut-SCF suffer much less from internal instabilities compared with conventional SCF calculations. Additionally, we show that the new SCF algorithms can enhance single-reference methods, such as configuration interaction. Finally, we explore how quantum algorithms for optimization can be applied to the QUSO problems arising from the Hartree-Fock method. Four distinct hybrid-quantum classical approaches are introduced: GAS-SCF, QAOA-SCF, QA-SCF and DQI-SCF.