用量子费舍尔信息重新思考量子持续学习

中文摘要 AI 辅助

量子持续学习旨在训练量子模型处理序列任务而不丢失先前学到的知识。然而，变分量子分类器在非平稳任务分布下容易出现灾难性遗忘。我们提出了量子弹性权重巩固（QEWC），一种基于量子费舍尔信息（QFI）的正则化方法来减轻遗忘。与基于经典费舍尔信息（CFI）的传统弹性权重巩固不同，QEWC使用QFI量化参数化量子态的内在敏感性。我们在序列二分类任务训练的VQCs上评估QEWC，包括经典图像分类和量子相位分类任务。模拟表明无正则化的序列训练会导致严重遗忘，而基于CFI的EWC和基于QFI的QEWC都能改善对先前任务的保留。机理分析进一步表明两种方法施加不同的正则化几何：CFI选择性地作用于测量敏感方向，而QFI在参数空间上施加更密集的状态几何约束。在去极化噪声下，CFI值因测量统计退化而强烈抑制，而QFI保留噪声参数化量子态更稳定的敏感性结构。这些结果确立了QEWC作为一种通过量子态几何研究和减轻量子持续学习中遗忘的物理动机方法

英文摘要

Quantum continual learning aims to train quantum models on sequential tasks without losing previously learned knowledge. However, variational quantum classifiers (VQCs) are prone to catastrophic forgetting under nonstationary task distributions. We propose quantum elastic weight consolidation (QEWC), a quantum Fisher information (QFI)-informed regularization method for mitigating forgetting. Unlike conventional elastic weight consolidation based on classical Fisher information (CFI), which measures parameter importance through measurement-dependent output statistics, QEWC uses QFI to quantify the intrinsic sensitivity of the parameterized quantum state. This gives an information-geometric view in which important parameters are identified by the local response of the quantum state manifold. We evaluate QEWC on VQCs trained on sequential binary classification tasks, including classical image-classification and quantum phase-classification tasks. Simulations show that sequential training without regularization causes severe forgetting, while both CFI-based EWC and QFI-based QEWC improve retention of previous tasks. Mechanistic analyses further show that the two methods impose different regularization geometries: CFI acts selectively on measurement-sensitive directions, whereas QFI imposes a denser state-geometric constraint over parameter space. Under depolarizing noise, CFI values are strongly suppressed by degraded measurement statistics, while QFI preserves a more stable sensitivity structure of the noisy parameterized quantum state. These results establish QEWC as a physically motivated approach for studying and mitigating forgetting in quantum continual learning through quantum-state geometry.

发表机构

• School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院电气工程学院）
• Cross College Elite Program, National Cheng Kung University（成功学院精英计划，成功大学）
• National Center for High-Performance Computing , National Institutes of Applied Research (NIAR)（高性能计算中心，应用研究国立机构）
• Department of Electrophysics, National Yang Ming Chiao Tung University（电子物理系，交通大学）

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