Abstract
Correlation is an important information resource, which is often used as a fundamental quantity for modeling tasks in machine learning. Since correlation between quantum entangled systems often surpasses that between classical systems, quantum information processing methods show superiority that classical methods do not possess. In this paper, we study the virtue of entangled systems and propose a novel classification algorithm called Quantum Entanglement inspired the Classification Algorithm (QECA). Particularly, we use the joint probability derived from entangled systems to model correlation between features and categories, that is, Quantum Correlation (QC), and leverage it to develop a novel QC-induced Multi-layer Perceptron framework for classification tasks. Experimental results on four datasets from diverse domains show that QECA is significantly better than the baseline methods, which demonstrates that QC revealed by entangled systems can improve the classification performance of traditional algorithms.
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Notes
- 1.
The widely used Dirac notations are used in this paper, in which a unit vector \(\mathbf {v}\) and its transpose \(\mathbf {v}^{T}\) are denoted as a ket \(|v\rangle \) and a bra \(\langle v|\), respectively. \(\otimes \) denotes the tensor product.
- 2.
\(\{|+\rangle , |-\rangle \}\) denotes an arbitrary orthonormal basis of the 1-qubit Hilbert space \(\mathbb {C}^{2}\). \(\sigma _{3} = \sigma _{z}\) denotes Pauli matrix, and Pauli matrix refers to four common matrices, which are \(2\times 2\) matrix, each with its own mark, namely \(\sigma _{x}\equiv \sigma _{1}\equiv X\), \(\sigma _{y}\equiv \sigma _{2}\equiv Y\), \(\sigma _{z}\equiv \sigma _{3}\equiv Z\) and \(\sigma _{0}\equiv I\).
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Zhang, J. et al. (2022). Quantum Entanglement Inspired Correlation Learning for Classification. In: Gama, J., Li, T., Yu, Y., Chen, E., Zheng, Y., Teng, F. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2022. Lecture Notes in Computer Science(), vol 13281. Springer, Cham. https://doi.org/10.1007/978-3-031-05936-0_5
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