A QUANTUM APPROXIMATION ALGORITHM FOR COVARIANCE OF RANDOM VARIABLES

Authors

  • MICHAL KOREN School of Industrial Engineering and Management, Shenkar College of Engineering, Design, and Art, Ramat-Gan, Israel.
  • OR PERETZ School of Industrial Engineering and Management, Shenkar College of Engineering, Design, and Art, Ramat-Gan, Israel.

Keywords:

amplitude amplification, quantum fourier transform, grover diffusion operator, data analysis, machine learning

Abstract

Quantum computing is a promising emerging field in computational science, attracting significant international research interest. Data representation is crucial to the success of machine learning models, and covariance analysis to determine relationships between pairs of random variables is an essential step in exploratory data analysis. Here we introduce a novel quantum algorithm for covariance approximation and its circuit implementation for discrete-value vectors. The algorithm leverages vital components of quantum computing, including amplitude encoding, the Grover diffusion algorithm for amplitude amplification and the quantum Fourier transform. As a core innovation, we utilize two quantum states and their properties of superposition product states to estimate the covariance between input vectors. Evaluating the quantum algorithm’s performance over five discrete-value distributions, we found high levels of agreement between the classical and quantum computations, with maximum average errors averaging 0.153. Furthermore, the analysis revealed additional applications of the Grover diffusion operator to solve problems.

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Published

2024-08-01

How to Cite

KOREN, M., & PERETZ, O. (2024). A QUANTUM APPROXIMATION ALGORITHM FOR COVARIANCE OF RANDOM VARIABLES. Quantum Journal of Engineering, Science and Technology, 5(3), 14–30. Retrieved from https://qjoest.com/index.php/qjoest/article/view/149

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