Quantum inspired Machine Learning through Entanglement Entropy

Junwei Zhang, Zhao Li, Yinghui Wang +4 more

Sheng-Chen Bai, Yicheng Tang, Shi-Ju Ran

Given an image of a white shoe drawn on a blackboard, how are the white pixels deemed (say by human minds) to be informative for recognizing the shoe without any labeling information on the pixels? Here we investigate such a “white shoe” recognition problem from the perspective of tensor network (TN) machine learning and quantum entanglement. Utilizing a generative TN that captures the probability distribution of the features as quantum amplitudes, we propose an unsupervised recognition scheme of informative features with variations of entanglement entropy (EE) caused by designed measurements. In this way, a given sample, where the values of its features are statistically meaningless, is mapped to the variations of EE that statistically characterize the gain of information. We show that the EE variations identify the features that are critical to recognize this specific sample, and the EE itself reveals the information distribution of the probabilities represented by the TN model. The signs of the variations further reveal the entanglement structures among the features. We test the validity of our scheme on a toy dataset of strip images, the MNIST dataset of hand-drawn digits, the fashion-MNIST dataset of the pictures of fashion articles, and the images of nerve cord. Our scheme opens the avenue to the quantum-inspired and interpreted unsupervised learning, which can be applied to, e.g., image segmentation and object detection.

Dong-Ling Deng

Domenico Pomarico, Roberto Cilli, Alfonso Monaco +10 more

Quantum-enhanced machine learning, encompassing both quantum algorithms and quantum-inspired classical methods such as tensor networks, offers promising tools for extracting structure from complex, high-dimensional data. In this work, we study the training dynamics of Matrix Product State (MPS) classifiers applied to three-class problems, using both fashion MNIST and hyperspectral satellite imagery as representative datasets. We investigate the phenomenon of grokking, where generalization emerges suddenly after memorization, by tracking entanglement entropy, local magnetization, and model performance across training sweeps. Additionally, we employ information-theory tools to gain deeper insights: transfer entropy is used to reveal causal dependencies between label-specific quantum masks, while O-information captures the shift from synergistic to redundant correlations among class outputs. Our results show that grokking in the fashion MNIST task coincides with a sharp entanglement transition and a peak in redundant information, whereas the overfitted hyperspectral model retains synergistic, disordered behavior. These findings highlight the relevance of high-order information dynamics in quantum-inspired learning and emphasize the distinct learning behaviors that emerge in multi-class classification, offering a principled framework to interpret generalization in quantum machine learning architectures.

Ameya Khot, Taesic Kim, Alve Rahman Akash +2 more

Quantum machine learning (QML) is transforming the field of machine learning (ML), which typically utilizes a quantum computing such as gate model-based and annealing-based computing. Recently, Ising solver chips have been developed to emulate the superposition and entanglement properties of quantum physics using the current silicon manufacturing technologies. The chips have potential to solve complex combinatorial optimization problems (COP) with significantly low power consumption and price. This paper proposes quantum-inspired ML (QiML) framework that provides an approach to train the traditional ML models using a physics-based Ising solver chip to develop QiMLs. To validate the feasibility of the proposed framework, a quantum-inspired support vector machine (QiSVM) is developed and the results are compared with a quantum SVM trained by a commercial D-Wave quantum annealer and a conventional SVM to solve real-world problems. The proposed QiML framework will open new frontiers for advancing ML technologies for industry cyber-physical system applications.

Rikard Wadman