The introduction of Neural Quantum States (NQS) has recently given a new twist to variational Monte Carlo (VMC). The ability to systematically reduce the bias of the wave function ansatz renders the approach widely applicable. However, performant implementations are crucial to reach the numerical state of the art. Here, we present a Python codebase that supports arbitrary NQS architectures and model Hamiltonians. Additionally leveraging automatic differentiation, just-in-time compilation to accelerators, and distributed computing, it is designed to facilitate the composition of efficient NQS algorithms.
The introduction of Neural Quantum States (NQS) has recently given a new twist to variational Monte Carlo (VMC). The ability to systematically reduce the bias of the wave function ansatz renders the approach widely applicable. However, performant implementations are crucial to reach the numerical state of the art. Here, we present a Python codebase that supports arbitrary NQS architectures and model Hamiltonians. Additionally leveraging automatic differentiation, just-in-time compilation to accelerators, and distributed computing, it is designed to facilitate the composition of efficient NQS algorithms.
The introduction of Neural Quantum States (NQS) has recently given a new twist to variational Monte Carlo (VMC). The ability to systematically reduce the bias of the wave function ansatz renders the approach widely applicable. However, performant implementations are crucial to reach the numerical state of the art. Here, we present a Python codebase that supports arbitrary NQS architectures and model Hamiltonians. Additionally leveraging automatic differentiation, just-in-time compilation to accelerators, and distributed computing, it is designed to facilitate the composition of efficient NQS algorithms.
TitleVariational Monte Carlo for Ab Initio Electronic Structure with Neural Quantum States and Selective State-Space Models Overview This repository provides a research implementation of Variational Monte Carlo (VMC) for ab initio electronic-structure calculations using Neural Quantum States (NQS). The work focuses on stable natural-gradient optimization, physically motivated wavefunction constraints, and the exploration of alternative architectural inductive biases for modeling electronic correlation. The project is released as an exploratory research artifact. All results, limitations, and open questions are stated explicitly. The work is motivated by a central question in modern neural quantum chemistry:can alternative sequence-based architectures reduce the quadratic scaling bottleneck of electron–electron interaction modeling while preserving physical fidelity? Scientific Scope The framework targets: Atomic systems (H through Ne) Small molecules (e.g., H₂, LiH, H₂O) Exploratory extensions, including: Periodic boundary conditions Excited-state considerations Berry-phase estimation Entanglement diagnostics Time-dependent VMC via McLachlan’s variational principle At present, numerical validation is limited to a single-electron benchmark (Hydrogen) and is explicitly presented as a sanity check of the physics engine and optimization loop, not as evidence of improved expressivity for correlated fermions. Core Methodology The implementation follows the standard Variational Monte Carlo formalism, in which a parameterized wavefunctionψ is optimized by minimizing the energy expectation value Optimization is performed using Stochastic Reconfiguration (SR), a natural-gradient method that accounts for the geometry of the variational manifold and significantly improves stability compared to first-order optimizers. Key numerical features include: Log-domain arithmetic for wavefunction evaluation Stable determinant computation using slogdet Hutchinson trace estimation for Laplacian evaluation Explicit enforcement of Kato cusp conditions via analytic Jastrow factors Multi-determinant antisymmetric ansatz to satisfy fermionic exchange symmetry SSM-Backflow Hypothesis The primary research contribution explored in this repository is the SSM-Backflow hypothesis. Most contemporary NQS models (e.g., FermiNet, PauliNet) model electron–electron interactions using explicit quadratic aggregation, leading to O(Ne2)O(N_e^2)O(Ne2) computational complexity. This work investigates an alternative inductive bias: For each electron, neighboring electrons are sorted by inter-electron distance The resulting sequence is processed using a selective state-space model (SSM) inspired by Mamba architectures Correlation information is accumulated sequentially through a learned recurrence Aggregated messages are used to parameterize backflow transformations or orbital functions This approach yields a theoretical complexity of O(NelogNe)O(N_e \log N_e)O(NelogNe) per layer (dominated by sorting) and is motivated by the physical observation that electronic correlation typically decays approximately exponentially with distance. Importantly, this is treated strictly as a hypothesis. The manuscript explicitly notes that: SSMs are not permutation-invariant by construction Sequential ordering may introduce inductive biases misaligned with fermionic symmetry Empirical validation on multi-electron systems is required before drawing conclusions Results and Current Validation Status At present, the repository reports results for atomic hydrogen (Ne = 1): Exact energy: −0.500000 Ha Achieved energy: −0.5001 Ha Error: 0.12 mHa (well below chemical accuracy) Local-energy variance: 0.0454 Optimizer: Stochastic Reconfiguration Convergence: ~100 optimization steps Because hydrogen has no electron–electron correlation, this result is interpreted solely as a sanity check of: Hamiltonian implementation Local-energy estimator Natural-gradient optimization loop Numerical stability mechanisms The manuscript clearly states that multi-electron benchmarks (e.g., He, Li, or H₂) are required to meaningfully evaluate the SSM-Backflow hypothesis and are planned for future versions. Stability and Diagnostics The implementation includes multiple practical safeguards designed to stabilize VMC optimization: Dynamic energy-based divergence detection Variance-based walker reset mechanisms Controlled respawning of walkers near nuclear centers In addition, an exploratory commutator-based diagnostic (informally termed the “Noether Inverse”) is included as a monitoring signal during training. This quantity is explicitly not claimed to represent a new conserved symmetry and is treated purely as an empirical observation requiring further theoretical and numerical investigation. Intended Use and Limitations This repository is released as: A research implementation A transparent record of an ongoing investigation A foundation for future validation and benchmarking It is not presented as a production-ready electronic-structure solver, nor as evidence of state-of-the-art performance. All limitations are explicitly documented in the manuscript. Licensing and Reuse The work is shared to encourage: Reproducibility Methodological discussion Extension and validation by the community If you use or build upon this work, please cite the Zenodo DOI associated with this release.
Neural quantum states (NQS) provide a flexible and highly expressive parameterization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic energies remains almost exclusively based on variational Monte Carlo (VMC). While VMC is effective for structured systems such as spin chains, its accuracy and efficiency for electronic Hamiltonians are hindered by sharply peaked distributions, stochastic gradient noise, and slow convergence with sample size. In this letter, we assess the capability of NQS-VMC to efficiently capture correlation in electronic ground states by comparing it to a recently developed NQS-based selected configuration (NQS-SC) approach. We set up a systematic comparison of the ground-state optimizations obtained with NQS-VMC and NQS-SC for molecular systems dominated by either static or dynamical correlation. The comparison demonstrates a clear advantage of NQS-SC over NQS-VMC in both energy accuracy and wave-function coefficients, particularly for statically correlated molecules. Moreover, NQS-SC exhibits robust systematic improvability, whereas NQS-VMC does not. These findings position NQS-SC as the new default approach over NQS-VMC for electronic structure calculations. We further observe that neither NQS-SC nor NQS-VMC can efficiently capture dynamical correlation, highlighting the need for future hybrid methods, such as multiconfigurational perturbation theories built on top of NQS solutions.
We present jQMC, a Python-based computational package for {\it ab initio} Quantum Monte Carlo (QMC) simulations, designed for modern GPU-accelerated computing environments. jQMC implements two well-established QMC algorithms: Variational Monte Carlo (VMC) and the lattice-regularized variant of Diffusion Monte Carlo (LRDMC). The employed wave function is a Jastrow factor combined with the antisymmetrized geminal power with spin-singlet and spin-triplet pairings, which contains the single Slater determinant as its special lowest-rank case. The wave function can be initialized from external Hartree-Fock/Density Functional Theory calculations through the TREX-IO library (a common wave-function format across electronic-structure packages) and optimized by stochastic reconfiguration and linear-method energy minimization. One of the prominent features of jQMC is its use of JAX, which enables automatic differentiation for wave function optimization and atomic force calculations, and allows the main QMC algorithms to be Just-In-Time (JIT) compiled and portable across CPU and GPU. jQMC is vectorized over walkers at the top level of the QMC algorithms, providing efficient intra-GPU~(CPU) vectorization. The multi-GPU~(CPU) parallelization is also supported through MPI and JAX sharding. To assess the practical performance of this implementation, we benchmarked jQMC performance on NVIDIA GPUs (A100 and H100) and analyzed CUDA kernels. For the test cases analyzed here, with system sizes up to 160 electrons, the current version of jQMC is faster than TurboRVB, a Fortran90 code implementing the same algorithms and wave functions, once jQMC is run on GPUs. In terms of wall-time, the gain can reach an order of magnitude for VMC, while it is more moderate for LRDMC.
Neural quantum states (NQS) provide a flexible and highly expressive parametrization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic energies remains almost exclusively based on variational Monte Carlo (VMC). While VMC is effective for structured systems such as spin chains, its accuracy and efficiency for electronic Hamiltonians are hindered by sharply peaked distributions, stochastic gradient noise, and slow convergence with sample size. In this Letter, we assess the capability of NQS-VMC to efficiently capture correlation in electronic ground states by comparing it to a recently developed NQS-based selected configuration (NQS-SC) approach. We set up a systematic comparison of the ground-state optimizations obtained with NQS-VMC and NQS-SC for molecular systems dominated by either static or dynamical correlation. The comparison demonstrates a clear advantage of NQS-SC over NQS-VMC in both energy accuracy and wave function coefficients, particularly for statically correlated molecules. Moreover, NQS-SC exhibits robust systematic improvability, whereas NQS-VMC does not. These findings position NQS-SC as the new default approach over NQS-VMC for electronic structure calculations. We further observe that neither NQS-SC nor NQS-VMC can efficiently capture dynamical correlation, highlighting the need for future hybrid methods, such as multiconfigurational perturbation theories built on top of NQS solutions.
Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architectures can support fast, accurate, and computationally accessible neural quantum state simulations. Using autoregressive recurrent wave functions together with recent advances in parallelizable recurrence, we develop variational ansätze, called parallel scan recurrent neural quantum states (PSR-NQS), which can be trained efficiently within variational Monte Carlo in one and two spatial dimensions. We demonstrate accurate benchmark results and show that, with iterative retraining, our approach reaches two-dimensional spin lattices as large as 52×52 while remaining in agreement with available quantum Monte Carlo data. Our results establish recurrent architectures as a practical and promising route toward scalable neural quantum state simulations with modest computational resources.