Foundation Neural-Network Quantum States (2502.09488v2)

Abstract: Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we propose Foundation Neural-Network Quantum States (FNQS) as an integrated paradigm for studying quantum many-body systems. FNQS leverage key principles of foundation models to define variational wave functions based on a single, versatile architecture that processes multimodal inputs, including spin configurations and Hamiltonian physical couplings. Unlike specialized architectures tailored for individual Hamiltonians, FNQS can generalize to physical Hamiltonians beyond those encountered during training, offering a unified framework adaptable to various quantum systems and tasks. FNQS enable the efficient estimation of quantities that are traditionally challenging or computationally intensive to calculate using conventional methods, particularly disorder-averaged observables. Furthermore, the fidelity susceptibility can be easily obtained to uncover quantum phase transitions without prior knowledge of order parameters. These pretrained models can be efficiently fine-tuned for specific quantum systems. The architectures trained in this paper are publicly available at https://huggingface.co/nqs-models, along with examples for implementing these neural networks in NetKet.

• The paper introduces Foundation Neural-Network Quantum States (FNQS), a framework that generalizes across different quantum systems by embedding Hamiltonian parameters into the neural network input.
• FNQS enables unsupervised detection of quantum phase transitions through the computation of fidelity susceptibility using embedded parameters.
• Numerical results demonstrate FNQS effectiveness in modeling systems like Ising and Heisenberg models, showing robust generalization and scalability.

Foundation Neural-Network Quantum States

The paper under discussion introduces the concept of Foundation Neural-Network Quantum States (FNQS), which draws parallels from the success of foundation models seen in machine learning, particularly within the domain of language and image processing. Foundation models, which include architectures like Transformers, exhibit powerful generalization capabilities across various tasks, leading the authors to explore their application in quantum many-body systems. This exploration marks a significant shift in the paradigm of how such quantum systems are studied, proposing a unified approach that integrates multimodal data inputs directly into the design of variational wave functions.

Summary of Key Contributions

The FNQS framework extends the applicability of neural networks as variational wave functions by embedding coupling constants into the neural architecture's input, allowing for the wave functions to adapt dynamically to different Hamiltonians. This is a notable innovation compared to traditional neural network quantum states (NQS) which are tailored for specific Hamiltonians.

1. Multimodal Inputs: The ability to handle multimodal inputs, such as incorporating both spin configurations and Hamiltonian couplings, is central to the FNQS design. This allows the model to generalize across different quantum systems, even for Hamiltonians it was not explicitly trained on.
2. Generalization and Scalability: FNQS exhibit robust generalization capabilities. The models can be pretrained on a set of systems and efficiently fine-tuned to adapt to unseen Hamiltonians. This aspect bears resemblance to transfer learning approaches in classical machine learning, significantly reducing the computational load associated with training separate models for each specific system.
3. Theoretical and Computational Implications: The theoretical framework introduces extensions to existing variational optimization methods, such as Stochastic Reconfiguration, allowing simultaneous optimization over multiple realizations or parameter sets of the quantum system. This extension is computationally efficient and makes the approach scalable to large quantum systems with disorder.
4. Fidelity Susceptibility and Unsupervised Phase Transition Detection: One of the standout features of the FNQS framework is its ability to compute the fidelity susceptibility using the embedded Hamiltonian parameters. This enables unsupervised detection of quantum phase transitions without pre-existing knowledge of the system's order parameters, offering a novel tool for theoretical exploration and analysis of complex quantum systems.

Numerical Results and Applications

The paper demonstrates the efficacy of FNQS through a series of numerical experiments, validating its performance in various quantum many-body systems, including:

• Ising Models: FNQS were applied to both one-dimensional transverse field Ising models and their disordered counterparts, showing accurate generalization across different phases and critical points. The ability to predict disordered-averaged quantities more efficiently than with conventional methods was particularly highlighted.
• $J_1$-$J_2$-$J_3$ Heisenberg Model: Through the computation of fidelity susceptibility, the FNQS was able to map out the complex phase diagram of the square lattice Heisenberg model, distinguishing between N\'eel, stripe, and valence bond solid phases.

Future Prospects and Implications

The paper suggests several future directions for FNQS, including extending the framework to fermionic systems and incorporating time-dependence for the paper of quantum dynamics. The potential fusion of FNQS with quantum chemistry and condensed matter tasks underscores its place as a versatile and scalable approach in the broader context of quantum computing and simulation.

The integration of these ideas and the public availability of the FNQS models are likely to spur collaborative advancements and greater adoption across different fields of physics, showcasing how methodologies from classical AI can be effectively adapted to grapple with the nuances of quantum systems. The FNQS framework not only enhances computation capabilities but also enriches the theoretical understanding of complex quantum phenomena.