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New self-consistent field (SCF) algorithms are derived from Hartree-Fock theory, formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. These novel methods, QUBO-SCF and MaxCut-SCF, demonstrate improved stability and performance for quantum chemistry calculations.

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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.