Efficient quantum analytic nuclear gradients with double factorization.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Quantum Computing Algorithms

Background:

• Efficient Hamiltonian representations like double factorization are crucial for quantum algorithms in chemistry.
• Noisy Intermediate-Scale Quantum (NISQ) algorithms require reduced circuit depth and repetitions.

Purpose of the Study:

• To develop a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices.
• To improve the efficiency of computing nuclear gradients and derivative properties from double factorized Hamiltonians.

Main Methods:

• Utilized a Lagrangian-based method for density matrix evaluation.
• Applied double factorization of Hamiltonians for quantum algorithms.
• Conducted classical simulations of QM/MM systems with varying atom counts.

Main Results:

• Successfully recovered off-diagonal density matrix elements in large-scale QM/MM simulations.
• Demonstrated the accuracy and feasibility of the Lagrangian approach.
• Showcased efficiency gains in computing nuclear gradients.

Conclusions:

• The Lagrangian approach offers significant efficiency improvements for quantum chemistry simulations.
• This method is applicable to variational quantum eigensolver algorithms for tasks like transition state optimization and molecular dynamics.