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

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Quantum Computing

Background:

• Self-consistent field (SCF) algorithms are fundamental to quantum chemistry, posing complex nonlinear optimization challenges.
• Existing SCF methods can suffer from instabilities, particularly for challenging molecular systems.

Purpose of the Study:

• To develop novel SCF algorithms inspired by Hartree-Fock theory that leverage Quadratic Unconstrained Binary Optimization (QUBO) and MaxCut graph problems.
• To enhance the stability and efficiency of quantum chemical calculations.
• To explore the application of quantum optimization algorithms to SCF problems.

Main Methods:

• Derivation of Hartree-Fock-inspired SCF algorithms solvable as Quadratic Unconstrained Spin/Binary Optimization (QUSO/QUBO) problems.
• Reformulation of SCF optimization as MaxCut graph problems, solved via semidefinite programming.
• Numerical validation on hydroxide anion (OH-) and molecular nitrogen (N2), up to 220 qubits.
• Introduction of four hybrid quantum-classical approaches (GAS-SCF, QAOA-SCF, QA-SCF, DQI-SCF).

Main Results:

• QUBO-SCF and MaxCut-SCF exhibit significantly reduced internal instabilities compared to conventional SCF methods.
• The new algorithms demonstrate potential for enhancing single-reference methods like configuration interaction.
• Successful application to systems up to 220 spin-orbitals.

Conclusions:

• The QUBO-SCF and MaxCut-SCF approaches offer a robust alternative for solving the SCF problem in quantum chemistry.
• These methods provide performance guarantees and improved stability.
• Hybrid quantum-classical algorithms show promise for future quantum computational chemistry.