Symmetry-Blocked Matrix Product States as a Neural-Network Quantum-State Ansatz for Quantum Chemistry

Abstract

Neural-network quantum states (NNQS) provide a flexible variational framework for many-electron wave functions, but their performance in quantum chemistry depends strongly on whether the ansatz encodes the physical structure of the electronic Hilbert space. In this work, we introduce symmetry-blocked matrix product states (MPS) as neural-network quantum-state ansatzes, denoted QiankunNet-MPS, for ab initio quantum chemistry, explicitly enforcing the U(1) ⊗ U(1) particle-number symmetry of electronic Hamiltonians to eliminate unphysical configurations and reduce the number of variational parameters. We further develop batched autoregressive sampling for canonical MPS representations and a two-site sweeping optimization scheme that combines stochastic energy gradients with singular value decomposition (SVD)-based bond adaptation. Benchmarks on small molecules show ground-state energies comparable with density matrix renormalization group (DMRG) at the same bond dimensions, while Fe2S2 calculations illustrate how DMRG-initialized bond expansion and variance extrapolation can be used to assess the large-bond-dimension trend in a strongly correlated transition-metal active space.