Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model achieves speedups of over three orders of magnitude compared to ab initio methods and reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art.

In this work, we introduce the first type of non-Euclidean neural quantum state (NQS) ansatz, in the form of the hyperbolic GRU (a variant of recurrent neural networks (RNNs)), to be used in the Variational Monte Carlo method of approximating the ground state energy for quantum many-body systems. In particular, we examine the performances of NQS ansatzes constructed from both conventional or Euclidean RNN/GRU and from hyperbolic GRU in the prototypical settings of the one- and two-dimensional transverse field Ising models (TFIM) and the one-dimensional Heisenberg $J_1J_2$ and $J_1J_2J_3$ systems. By virtue of the fact that, for all of the experiments performed in this work, hyperbolic GRU can yield performances comparable to or better than Euclidean RNNs, which have been extensively studied in these settings in the literature, our work is a proof-of-concept for the viability of hyperbolic GRU as the first type of non-Euclidean NQS ansatz for quantum many-body systems. Furthermore, in settings where the Hamiltonian displays a clear hierarchical interaction structure, such as the 1D Heisenberg $J_1J_2$ & $J_1J_2J_3$ systems with the 1st, 2nd and even 3rd nearest neighbor interactions, our results show that hyperbolic GRU definitively outperforms its Euclidean version in almost all instances. The fact that these results are reminiscent of the established ones from natural language processing where hyperbolic GRU almost always outperforms Euclidean RNNs when the training data exhibit a tree-like or hierarchical structure leads us to hypothesize that hyperbolic GRU NQS ansatz would likely outperform Euclidean RNN/GRU NQS ansatz in quantum spin systems that involve different degrees of nearest neighbor interactions. Finally, with this work, we hope to initiate future studies of other types of non-Euclidean NQS beyond hyperbolic GRU.

We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks.

Obtaining accurate solutions to the Schrödinger equation is the key challenge in computational quantum chemistry. Deep-learning-based V ariational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy, but only at large computational cost.

Finding fast and accurate approaches to solving Schrödinger equations is a central challenge in quantum chemistry, with far-reaching implications for material science and pharmaceutical development. The ability to solve this equation precisely would unlock a plethora of properties inherent to the microscopic systems being studied.

A.1 Quantum chemistry At the center of quantum chemistry methods lies the electronic Schrödinger equation ˆ H

This accuracy makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner.

In this work, we benchmark \simulacra's synthetic data generation pipeline against a state-of-the-art Microsoft pipeline on a dataset of small to large systems. By analyzing the energy quality, autocorrelation times, and effective sample size, our findings show that Simulacra's Large Wavefunction Models (LWM) pipeline, paired with state-of-the-art Variational Monte Carlo (VMC) sampling algorithms, reduces data generation costs by 15-50x, while maintaining parity in energy accuracy, and 2-3x compared to traditional CCSD methods on the scale of amino acids. This enables the creation of affordable, large-scale \textit{ab-initio} datasets, accelerating AI-driven optimization and discovery in the pharmaceutical industry and beyond. Our improvements are based on a novel and proprietary sampling scheme called Replica Exchange with Langevin Adaptive eXploration (RELAX).