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

Accurately solving the Schrödinger equation for intricate systems remains a prominent challenge in physical sciences. Here we present QiankunNet, a neural network quantum state (NNQS) framework that combines Transformer architectures with efficient autoregressive sampling to solve the many-electron Schrödinger equation. At its core is a Transformer-based wave function ansatz that captures complex quantum correlations through attention mechanisms, effectively learning the structure of many-body states. The quantum state sampling employs layer-wise Monte Carlo tree search (MCTS) that naturally enforces electron number conservation while exploring orbital configurations. The framework incorporates physics-informed initialization using truncated configuration interaction solutions, providing principled starting points for variational optimization. Our systematic benchmarks demonstrate QiankunNet's versatility across different chemical systems. For molecular systems up to 30 spin orbitals, we achieved correlation energies reaching 99.9% of the full configuration interaction (FCI) benchmark, setting a new standard for neural network quantum states. Most notably, in treating the Fenton reaction mechanism, a fundamental process in biological oxidative stress, QiankunNet successfully handled a large CAS(46e,26o) active space, enabling accurate description of the complex electronic structure evolution during Fe(II) to Fe(III) oxidation.