Hamiltonian-Informed Point Group Symmetry-Respecting Ansätze for the Variational Quantum Eigensolver

Area of Science:

• Quantum Chemistry
• Computational Quantum Physics

Background:

• Variational Quantum Eigensolver (VQE) utilizes point group symmetry for compact ansätze on Noisy Intermediate-Scale Quantum (NISQ) devices.
• Symmetry-reduced Unitary Coupled Cluster Singles and Doubles (SymUCCSD) is limited to Abelian point groups and can be deficient for non-Abelian systems.

Purpose of the Study:

• To develop a novel, shallow quantum ansatz for VQE applicable to a broader range of molecular symmetries.
• To improve the efficiency and scalability of quantum computations for molecular energy levels.

Main Methods:

• Propose Hamiltonian-informed UCCSD (HiUCCSD), an ansatz engineered using information from the molecular Hamiltonian.
• Theoretically validate HiUCCSD for Abelian point groups.
• Numerically assess HiUCCSD performance on 10 molecular systems with diverse symmetries, including non-Abelian cases.

Main Results:

• HiUCCSD demonstrates effectiveness for both Abelian and non-Abelian point group systems.
• Significant reductions in parameter count (18-83%) and circuit size (26-83%) for VQE compared to standard UCCSD.
• Reduced excitation operator pool size (27-84%) for ADAPT-VQE across studied molecules.

Conclusions:

• HiUCCSD offers superior performance and broader applicability than existing methods.
• The novel ansatz facilitates efficient large-scale molecular VQE implementations on NISQ devices.