Solving the many-electron Schrödinger equation with a transformer-based framework

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• Solving the Schrödinger equation for complex quantum systems is computationally demanding.
• Accurate modeling of electron correlations is crucial for understanding chemical behavior.

Purpose of the Study:

• To introduce QiankunNet, a novel neural network quantum state (NNQS) framework for solving the many-electron Schrödinger equation.
• To demonstrate the framework's capability in accurately describing complex electronic structures and quantum correlations.

Main Methods:

• Utilizing Transformer architectures for a wave function ansatz to capture quantum correlations.
• Employing efficient autoregressive sampling with layer-wise Monte Carlo tree search (MCTS) for quantum state exploration.
• Incorporating physics-informed initialization using truncated configuration interaction (CI) solutions.

Main Results:

• Achieved 99.9% of full configuration interaction (FCI) benchmark correlation energies for molecular systems up to 30 spin orbitals.
• Successfully treated a large CAS(46e,26o) active space for the Fenton reaction mechanism.
• Demonstrated high accuracy and versatility across various chemical systems.

Conclusions:

• QiankunNet sets a new standard for NNQS accuracy in quantum chemistry.
• The framework enables precise modeling of complex electronic structures, crucial for processes like the Fenton reaction.
• QiankunNet offers a powerful tool for advancing physical sciences through accurate quantum mechanical simulations.