Importance-Reweighted Fock-Space Variational Monte Carlo

Abstract

Fock-space variational Monte Carlo (FS-VMC) evaluates variational quantities by stochastic sampling over discrete many-body configurations. For ab initio electronic Hamiltonians, Born distributions can differ markedly between systems, and a Markov chain that mixes well need not yield low-variance estimators. We introduce importance-reweighted FS-VMC (IR-FS-VMC), which leaves the variational objective unchanged while redesigning its Monte Carlo evaluation. An auxiliary distribution and Hamiltonian-guided proposal define the Markov chain, while an evaluation Markov kernel defines an analytically tractable evaluation distribution. Self-normalized importance reweighting then recovers the Born-distribution expectations entering the energy, gradient, and stochastic reconfiguration (SR) matrix. Controlled comparisons on equilibrium H2O and Fe2S2 separate Markov-chain acceptance from local-energy fluctuations and optimization behavior. Using one production protocol, calculations for H2O dissociation, 36-site hydrogen lattices, and Fe2S2 and Fe4S4 active spaces yield accurate variational energies across different Born distributions and electronic-correlation regimes. Together, these results show that the production protocol can support robust FS-VMC optimization across the electronic-structure regimes studied here.