When Less is More: Approximating the Quantum Geometric Tensor with Block Structures

2025/10/09 by Ahmedeo Shokry, Shokry, Ahmedeo, Alessandro Santini +3
Computer Science · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2510.08430

openalex publication_date 2025/10/09 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

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 J₁-J₂ models show faster convergence, lower energy, and improved stability.

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