Nonunitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation.

Area of Science:

• Quantum chemistry
• Computational chemistry
• Quantum computing applications

Background:

• Accurately describing strongly correlated systems on quantum computers is challenging due to resource limitations.
• Hardware-efficient ansatzes (HEA) are resource-efficient but often lack correlation accuracy.
• Nonunitary VQE (nuVQE) with Hartree-Fock states improves correlation but has limitations.

Purpose of the Study:

• To introduce and evaluate the Localized Active Space Self-Consistent Field (LASSCF) combined with nuVQE (LAS-nuVQE) for quantum chemistry.
• To assess the accuracy and resource efficiency of LAS-nuVQE for strongly correlated systems.
• To address symmetry breaking and measurement overhead in nuVQE for practical quantum simulations.

Main Methods:

• Implemented LASSCF as an initial state for nuVQE calculations.
• Developed spin-constrained LAS-nuVQE to ensure spin-pure results.
• Utilized Pauli grouping and shot-frugal sampling to mitigate measurement costs.

Main Results:

• LAS-nuVQE achieved chemical accuracy with fewer than 70 gates for H4 and square cyclobutadiene (C4H4).
• The method recovered interfragment correlations and outperformed standard HEA.
• Spin-constrained LAS-nuVQE provided spin-pure results, and measurement mitigation reduced costs by up to two orders of magnitude.
• LAS-nuVQE demonstrated improved accuracy and reduced computational time compared to vanilla VQE.

Conclusions:

• LAS-nuVQE presents a practical pathway for accurate multireference chemical simulations on current quantum hardware.
• The approach achieves both accuracy and affordability for challenging correlated systems.
• This work advances the application of quantum computing in chemistry by optimizing resource utilization and result fidelity.