Better accuracy with fewer qubits: Single-particle basis set optimization for quantum chemistry on quantum computers

As quantum computers remain noisy and limited in qubit capacity, researchers face a trade-off between basis set quality and the ability to perform accurate quantum chemical calculations. This paper investigates whether re-optimizing minimal basis sets—specifically the contraction coefficients and exponents of Gaussian-type orbitals—can provide higher accuracy for a fixed number of qubits compared to standard basis sets like 6-31G or Dunning's cc-pVQZ.

The authors introduce a memetic algorithm that combines a genetic algorithm (for global exploration) with an aggressive gradient-free refinement strategy (for local optimization). They apply this to generate modified minimal basis sets, termed MSTO-kG (where k ranges from 2 to 11), for atoms from Hydrogen through Fluorine. By using these optimized parameters, they perform Full Configuration Interaction (FCI) calculations and compare the resulting ground state energies and quantum resource requirements (qubits, two-qubit gates, and T-gates) against traditional basis sets when implemented in algorithms like VQE, QPE, and HHL.

The MSTO-kG basis sets consistently yield ground state energies that are comparable to or better than those obtained using 6-31G basis sets. For the Lithium atom, the MSTO bases even outperform the high-quality cc-pVQZ basis sets while using the same number of qubits. When applied to molecular systems like Li2, LiH, and BeH2, the MSTO bases maintain this performance advantage. Furthermore, resource estimation shows that these optimized bases significantly reduce the number of two-qubit gates and logical T-gates required for quantum algorithms, making them highly efficient for near-term quantum hardware.

This work provides a practical pathway to improve the accuracy of quantum chemistry simulations on NISQ-era hardware without increasing the qubit count. By shifting the computational burden to a one-time classical pre-processing step (basis set optimization), researchers can extract more physical information from limited quantum resources, potentially accelerating the development of quantum applications in materials science and drug discovery.