In supervised learning, the generative approach is an important one, which obtains the generative model by learning the joint probability between features and categories. In quantum mechanics, Quantum Entanglement (QE) can provide a statistical correlation between subsystems (or attributes) that is stronger than what classical systems are able to produce. It inspires us to use entangled systems (states) to characterize this strong statistical correlation between features and categories, that is, to use the joint probability derived from QE to model the correlation. Based on the separability of the density matrix of entangled systems, this paper formally clarifies the manifestation of the strong statistical correlation revealed by QE, and implements a classification algorithm (called ECA) to verify the feasibility and superiority of the correlation in specific tasks. Since QE arises from the measurement process of entangled systems, the core of ECA is quantum measurement operations. In this paper, we use the GHZ [25] and W [22] states to prepare the entangled system and use a fully connected network layer to learn the measurement operator. It can also be understood as replacing the output layer of the Multi-Layer Perceptron (MLP) with a quantum measurement operation. The experimental results show that ECA is superior to most representative classification algorithms in multiple evaluation metrics.
In supervised learning, the generative approach is an important one, which obtains the generative model by learning the joint probability between features and categories. In quantum mechanics, Quantum Entanglement (QE) can provide a statistical correlation between subsystems (or attributes) that is stronger than what classical systems are able to produce. It inspires us to use entangled systems (states) to characterize this strong statistical correlation between features and categories, that is, to use the joint probability derived from QE to model the correlation. Based on the separability of the density matrix of entangled systems, this paper formally clarifies the manifestation of the strong statistical correlation revealed by QE, and implements a classification algorithm (called ECA) to verify the feasibility and superiority of the correlation in specific tasks. Since QE arises from the measurement process of entangled systems, the core of ECA is quantum measurement operations. In this paper, we use the GHZ [25] and W [22] states to prepare the entangled system and use a fully connected network layer to learn the measurement operator. It can also be understood as replacing the output layer of the Multi-Layer Perceptron (MLP) with a quantum measurement operation. The experimental results show that ECA is superior to most representative classification algorithms in multiple evaluation metrics.
In machine learning, classification algorithms often use statistical methods to build the correspondence between features (or attributes) and categories (or labels), that is, the statistical correlation between features and categories. In quantum theory, a large number of experimental results show that quantum correlation is far stronger than what can be explained by local hidden theory (i.e., classical or non-quantum theory), that is, quantum mechanics theory reveals a statistical correlation stronger than that described by classical theory. Based on this, this paper will use the strong statistical correlation revealed by Bell state to build a classification algorithm to verify the validity and superiority of the formal framework of quantum mechanics in specific classification tasks. Specifically, we use quantum joint probabilities derived from the measurement process of Bell state to model the quantum statistical correlation between features and categories. The paper first theoretically proves that the formal framework used has the ability to violate Bell inequality; moreover, a classification algorithm is implemented and verified on classic machine learning datasets. Experimental results show that the algorithm is significantly better than most mainstream machine learning algorithms.
Neural Networks (NNs) have received extensive attention and research due to their ability to extract and combine different features non-manually and to mine the internal relationships between features. In quantum mechanics, the entangled state simultaneously describes the classical and non-classical correlation between subsystems, so it can reveal important quantum phenomena such as non-locality, entanglement, etc., but its essence is the characterization of strong statistical relationships. Considering the superiority of the entangled state, this article attempts to use the entangled state to reconstruct the neurons of NNs to achieve that the network model can characterize the strong statistical relationship between the features, namely, the classical and non-classical correlation. Specifically, based on concurrence, a quantification method of entanglement, we propose a regularizer that can constrain a state vector to an entangled state, and apply it to the optimization process to ensure that the vector passed to the neuron is a legal entangled state. Finally, the entangled state is measured to obtain the output of the neuron. Experimental results show that our model is better than the baseline. Moreover, it performs well compared to the model inspired by quantum entanglement.
Quantum Machine Learning (QML) has emerged as a promising framework for exploring how quantum dynamics may enhance data processing tasks. Here we investigate Quantum Extreme Learning Machines (QELMs), a quantum analogue of classical Extreme Learning Machines in which training is restricted to the output layer. Our architecture combines dimensionality reduction (via PCA or Autoencoders), quantum state encoding, evolution under an XX Hamiltonian, and projective measurement to produce features for a classical single-layer classifier. By analyzing the classification accuracy as a function of evolution time, we observe a sharp transition between low- and high-accuracy regimes, followed by saturation. Remarkably, the saturated performance is comparable to that obtained using Haar-random unitaries that generate maximally complex dynamics, even though the XX model is integrable and local. Our results indicate that this increase in performance correlates with the onset of entanglement, which improves the embedding of classical data in Hilbert space and leads to more separable clusters in measurement probability space. Thus, moderate entanglement can contribute positively to the structure of the data representation, improving learnability without necessarily implying quantum computational advantage. For the image-classification tasks studied here, namely MNIST, Fashion-MNIST, and CIFAR-10, the relevant evolution time is consistent with information exchange over short distances and, within the explored system sizes, does not show evidence of scaling with the full system size. This suggests that QELM performance in this regime relies only on limited entanglement and remains compatible with efficient classical simulation. Our results clarify how local quantum dynamics and moderate quantum correlations are already sufficient to generate useful feature representations for learning.
Abstract Quantum information theory, and in particular, the theory of quantum state discrimination, has enabled the development of a supervised multi-class classification algorithm. Inspired by the Pretty Good Measurement (PGM), a quantum-inspired classifier named the PGM Classifier has been designed, capable of classifying among multiple classes without resorting to the One versus One or One versus Rest strategy. In the recent past, several approaches of quantum machine learning have been introduced to classify entangled and separable states. In this article, we apply the PGM Classifier to discriminate among factorized states, separable states, and entangled states. We analyze from the simplest case ( 2 qubits) up to a system of ( 5 qubits) and offer a comparison between our quantum-inspired classifier and other classical classifiers. Finally, we propose a refined classification of non-locality based on the violation of the Mermin and Svetlichny inequalities.
This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the relationship between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the output. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings.
Entanglement is a key quantity for characterizing quantum correlations in particle scattering processes, but its direct evaluation is computationally demanding on quantum hardware. In this work, we investigate whether fermion density profiles, which are easier to access, can serve as proxies for entanglement by framing the problem as a classification task across multiple entanglement thresholds. Using the fermion scattering in the Thirring model as a test bed, we compare Quantum Convolutional Neural Networks (QCNNs) with classical CNNs of comparable parameter counts, and find that QCNNs achieve consistently competitive or superior accuracy with faster convergence and lower variance. Notably, we observe that increasing the model size does not improve the performance within the architectures studied here, and larger models appear to be more sensitive to the choice of encoding. Instead, a compact 4-qubits QCNN provides the best results, suggesting the importance of trainability and encoding choices over model scaling. These findings demonstrate the potential of quantum and quantum-inspired machine learning models for extracting nontrivial quantum information from accessible observables, with implications for high-energy physics and quantum many-body systems.