When Less is More: Approximating the Quantum Geometric Tensor with Block Structures
Quantum Physics
2025-11-05 v2 Disordered Systems and Neural Networks
Computational Physics
Abstract
The natural gradient is central in neural quantum states optimizations but it is limited by the cost of computing and inverting the quantum geometric tensor, the quantum analogue of the Fisher information matrix. We introduce a block-diagonal quantum geometric tensor that partitions the metric by network layers, analogous to block-structured Fisher methods such as K-FAC. This layer-wise approximation preserves essential curvature while removing noisy cross-layer correlations, improving conditioning and scalability. Experiments on Heisenberg and frustrated - models show faster convergence, lower energy, and improved stability.
Cite
@article{arxiv.2510.08430,
title = {When Less is More: Approximating the Quantum Geometric Tensor with Block Structures},
author = {Ahmedeo Shokry and Alessandro Santini and Filippo Vicentini},
journal= {arXiv preprint arXiv:2510.08430},
year = {2025}
}