A New Approach for Quantum Phase Estimation Based Algorithms for Machine Learning

One of the greatest developments in computer science is undoubtedly quantum computing. It has demonstrated to give various benefits over the classical algorithms, particularly in the significant reduction of processing time, due to the parallelism and entanglement properties. One of the most crucial quantum computing algorithms is quantum phase estimation (QPE). It is called the eigenvalue finding module for unitary operators. It has helped to solve the order finding and the factoring problem, and to calculate the eigenvalues of unitary matrices and quantum sampling methods. In this paper, we study recent improved versions for the QPE procedure, their advantages and experimentation. We also propose a new approach for QPE based algorithms for machine learning (ML). These algorithms are the Harrow-Hassidim-Lloyd (HHL) algorithm for solving linear systems, the quantum singular value thresholding (QSVT) algorithm for matrix completion in recommender systems, and the quantum principal components analysis (QPCA) for data visualization.