Quantum machine learning algorithms based on linear algebra

Many quantum machine learning algorithms are based on variants of quantum algorithms for solving linear equations, which can efficiently solve N-variable linear equations with complexity of O(log2 N) under certain conditions. The quantum matrix inversion algorithm can accelerate many machine learning methods, such as least square linear regression, least square version of support vector machine, Gaussian process, and more. The training of these algorithms can be simplified to solve linear equations. The key bottleneck of this type of quantum machine learning algorithms is data input—that is, how to initialize the quantum system with the entire data set. Although efficient data-input algorithms exist for certain situations, how to efficiently input data into a quantum system is as yet unknown for most cases.