Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions

TL;DR

This paper introduces two neural quantum state architectures, SCALE and ACE, that significantly improve efficiency and accuracy for simulating large strongly correlated lattice fermion systems, enabling new scientific insights.

Contribution

The paper presents SCALE and ACE, novel neural quantum state architectures that achieve state-of-the-art efficiency and accuracy in large-scale fermionic simulations.

Findings

SCALE reduces computational scaling from O(N^4) to O(N^3) and speeds up calculations by over 40 times.

ACE achieves unprecedented accuracy on large systems, surpassing recent methods.

SCALE and ACE enable exploration of large lattice fermion models previously inaccessible.

Abstract

Neural Quantum States (NQS) are now among the most accurate methods for studying strongly correlated many-fermion systems, outperforming existing many-body approaches for large systems. However, NQS calculations remain extremely resource-intensive. Here, we introduce a new Pareto frontier of efficiency and accuracy for NQS in simulating strongly correlated lattice fermions, defined by two complementary backflow-related architectures: the Sparse Convolutional Ansatz for Lattice Electrons (SCALE) (state-of-the-art efficiency) and the Accurate Convolutional ansatz for lattice Electrons (ACE) (state-of-the-art accuracy), benchmarked on the iconic Hubbard and $t-J$ models for large lattices. SCALE uses a tailored convolutional design enabling efficient local updates via low-rank determinant updates, reducing computational scaling from $O(N^4)$ to $O(N^3)$ in backflow methods and yielding a >40$\times$ practical speed-up in tests while maintaining high variational accuracy. As an application, we study the previously inaccessible 1/8-doped pure Hubbard model up to $32 \times 32$, finding no significant energy difference between horizontal and vertical filled stripe states - contrasting with half-filled stripe states when next-nearest-neighbor hoppings are included. ACE employs a deep convolutional stack to maximize expressive power, achieving unprecedented accuracy on large systems. Extensive benchmarks on Hubbard and $t-J$ models show SCALE delivers variational energies competitive with leading methods at a fraction of the cost, while ACE sets a new accuracy benchmark, surpassing recent results with only 1/6 the runtime for $16 \times 4$ systems. These new NQS approaches provide scalable, affordable, and accurate tools for exploring strongly correlated fermionic physics, such as the microscopic mechanism of unconventional superconductivity.