Quantum Recurrence Plot Algorithm Based on Quantum Principal Component Analysis

• URL: http://arxiv.org/abs/2607.07056v1
• Date: Wed, 08 Jul 2026 06:32:45 GMT
• Title: Quantum Recurrence Plot Algorithm Based on Quantum Principal Component Analysis
• Abstract summary: We improve the distance threshold function of the recurrence plot algorithm using a density operator.<n>We integrate it with quantum circuits, and thereby develop a Quantum Recurrence Plot (QRP) algorithm.
• Score: 1.6459390478878912
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recurrence Plot (RP) is a method employed to analyze the periodicity, chaoticity, and nonlinear characteristics of complex systems. Quantum Principal Component Analysis (QPCA), on the other hand, achieves dimensionality reduction of sample data using density matrices based on quantum circuits. We improve the distance threshold function of the recurrence plot algorithm using a density operator conceptually equivalent to the covariance matrix, integrate it with quantum circuits, and thereby develop a Quantum Recurrence Plot (QRP) algorithm. This algorithm achieves ultra-high efficiency in parallel computing, reduces computational costs, and simultaneously upgrades the traditional grayscale recurrence plot to colored heatmaps, enabling a better revelation of the system's dynamical characteristics.

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