NNQS-AFQMC: Neural Network Quantum States Enhanced Fermionic Quantum Monte Carlo.

Area of Science:

• Computational Chemistry
• Quantum Many-Body Physics
• Materials Science

Background:

• Neural network quantum states (NNQS) offer flexible representations of complex wave functions but are computationally expensive.
• Auxiliary-field quantum Monte Carlo (AFQMC) is a powerful method for ground-state calculations but relies on accurate trial wave functions.
• Integrating advanced wave function ansätze into AFQMC is crucial for improving accuracy in electronic structure calculations.

Purpose of the Study:

• To develop an efficient method for using NNQS as trial wave functions within AFQMC.
• To reduce the computational cost associated with NNQS optimization in quantum Monte Carlo simulations.
• To enhance the accuracy of AFQMC calculations for strongly correlated systems.

Main Methods:

• Direct integration of NNQS with AFQMC using stochastic sampling techniques.
• Implementing NNQS as trial wave functions to constrain AFQMC.
• Testing the NNQS-AFQMC methodology on the nitrogen molecule (N2) at stretched geometries.

Main Results:

• Achieved near-exact total energies for the nitrogen molecule using the NNQS-AFQMC method.
• Demonstrated manageable computational cost for NNQS-AFQMC, overcoming a key limitation of NNQS.
• Validated the effectiveness of NNQS as high-quality trial wave functions for AFQMC.

Conclusions:

• The NNQS-AFQMC method provides a computationally efficient and accurate approach for electronic structure calculations.
• This integration overcomes longstanding challenges in treating strongly correlated systems.
• The methodology shows significant promise for future applications in quantum chemistry and materials science.