This paper introduces the Quadratic Quantum Variational Monte Carlo (Q$^2$VMC) algorithm, an innovative algorithm in quantum chemistry that significantly enhances the efficiency and accuracy of solving the Schrödinger equation. Inspired by the discretization of imaginary-time Schrödinger evolution, Q$^2$VMC employs a novel quadratic update mechanism that integrates seamlessly with neural network-based ansatzes.

Chemistry may not be the'killer app' for quantum computers after all Quantum chemistry calculations that could advance drug development or agriculture have recently emerged as a promising "killer application" of quantum computers, but a new analysis suggests this is unlikely to be the case. Progress in building quantum computers has greatly accelerated in recent years, but it remains an open question what uses are most likely to justify the ongoing investment in this technology. One popular contender is solving problems in quantum chemistry, such as calculating the energy levels of molecules relevant for biomedicine or industry. This requires accounting for the behavior of many quantum particles - electrons in the molecule - simultaneously, so it seems like a good match for computers made from many quantum parts. Quantum computers have finally arrived, but will they ever be useful? However, Xavier Waintal at CEA Grenoble in France and his colleagues have now shown that two leading quantum computing algorithms for this task may actually have, at best, limited use.

Spin plays a fundamental role in understanding electronic structure, yet many real-space wavefunction methods fail to adequately consider it. We introduce the Spin-Adapted Antisymmetrization Method (SAAM), a general procedure that enforces exact total spin symmetry for antisymmetric many-electron wavefunctions in real space. In the context of neural network-based quantum Monte Carlo (NNQMC), SAAM leverages the expressiveness of deep neural networks to capture electron correlation while enforcing exact spin adaptation via group representation theory. This framework provides a principled route to embed physical priors into otherwise black-box neural network wavefunctions, yielding a compact representation of correlated system with neural network orbitals. Compared with existing treatments of spin in NNQMC, SAAM is more accurate and efficient, achieving exact spin purity without any additional tunable hyperparameters. To demonstrate its effectiveness, we apply SAAM to study the spin ladder of iron-sulfur clusters, a long-standing challenge for many-body methods due to their dense spectrum of nearly degenerate spin states. Our results reveal accurate resolution of low-lying spin states and spin gaps in [Fe$_2$S$_2$] and [Fe$_4$S$_4$] clusters, offering new insights into their electronic structures. In sum, these findings establish SAAM as a robust, hyperparameter-free standard for spin-adapted NNQMC, particularly for strongly correlated systems.

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.

Neural scaling laws are driving the machine learning community toward training ever-larger foundation models across domains, assuring high accuracy and transferable representations for extrapolative tasks. We test this promise in quantum chemistry by scaling model capacity and training data from quantum chemical calculations. As a generalization task, we evaluate the resulting models' predictions of the bond dissociation energy of neutral H$_2$, the simplest possible molecule. We find that, regardless of dataset size or model capacity, models trained only on stable structures fail dramatically to even qualitatively reproduce the H$_2$ energy curve. Only when compressed and stretched geometries are explicitly included in training do the predictions roughly resemble the correct shape. Nonetheless, the largest foundation models trained on the largest and most diverse datasets containing dissociating diatomics exhibit serious failures on simple diatomic molecules. Most strikingly, they cannot reproduce the trivial repulsive energy curve of two bare protons, revealing their failure to learn the basic Coulomb's law involved in electronic structure theory. These results suggest that scaling alone is insufficient for building reliable quantum chemical models.

Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms, whose performance is highly sensitive to parameter initialization. Although recent machine learning-based initialization methods have achieved state-of-the-art performance, their progress has been limited by the lack of comprehensive datasets. Existing resources are typically restricted to a single domain, contain only a few hundred instances, and lack complete coverage of Hamiltonians, ansatz circuits, and optimization trajectories. To overcome these limitations, we introduce VQEzy, the first large-scale dataset for VQE parameter initialization. VQEzy spans three major domains and seven representative tasks, comprising 12,110 instances with full VQE specifications and complete optimization trajectories. The dataset is available online, and will be continuously refined and expanded to support future research in VQE optimization.

Variational quantum Eigensolver (VQE) is a leading candidate for harnessing quantum computers to advance quantum chemistry and materials simulations, yet its training efficiency deteriorates rapidly for large Hamiltonians. Two issues underlie this bottleneck: (i) the no-cloning theorem imposes a linear growth in circuit evaluations with the number of parameters per gradient step; and (ii) deeper circuits encounter barren plateaus (BPs), leading to exponentially increasing measurement overheads. To address these challenges, here we propose a deep learning framework, dubbed Titan, which identifies and freezes inactive parameters of a given ansatze at initialization for a specific class of Hamiltonians, reducing the optimization overhead without sacrificing accuracy. The motivation of Titan starts with our empirical findings that a subset of parameters consistently has a negligible influence on training dynamics. Its design combines a theoretically grounded data construction strategy, ensuring each training example is informative and BP-resilient, with an adaptive neural architecture that generalizes across ansatze of varying sizes. Across benchmark transverse-field Ising models, Heisenberg models, and multiple molecule systems up to 30 qubits, Titan achieves up to 3 times faster convergence and 40% to 60% fewer circuit evaluations than state-of-the-art baselines, while matching or surpassing their estimation accuracy. By proactively trimming parameter space, Titan lowers hardware demands and offers a scalable path toward utilizing VQE to advance practical quantum chemistry and materials science.

Scaling laws have been used to describe how large language model (LLM) performance scales with model size, training data size, or amount of computational resources. Motivated by the fact that neural quantum states (NQS) has increasingly adopted LLM-based components, we seek to understand NQS scaling laws, thereby shedding light on the scalability and optimal performance--resource trade-offs of NQS ansatze. In particular, we identify scaling laws that predict the performance, as measured by absolute error and V-score, for transformer-based NQS as a function of problem size in second-quantized quantum chemistry applications. By performing analogous compute-constrained optimization of the obtained parametric curves, we find that the relationship between model size and training time is highly dependent on loss metric and ansatz, and does not follow the approximately linear relationship found for language models.

This paper introduces the Quadratic Quantum Variational Monte Carlo (Q 2 VMC) algorithm, an innovative algorithm in quantum chemistry that significantly enhances the efficiency and accuracy of solving the Schrödinger equation. Inspired by the discretization of imaginary-time Schrödinger evolution, Q 2 VMC employs a novel quadratic update mechanism that integrates seamlessly with neural network-based ansatzes. This study not only advances the field of computational quantum chemistry but also highlights the important role of discretized evolution in variational quantum algorithms, offering a scalable and robust framework for future quantum research.