ABSTRACT
The quantum algorithm for linear systems of equations for is one of the main fundamental algorithms expected to provide a speedup over their classical counterparts. HHL is going to be one of the most useful subroutines for any quantum machine learning algorithm because almost all machine learning uses some form of a linear system of equations. This chapter describes the HHL algorithm, gives an example step by step using qiskit command HamiltonianGate, and indicates the constrains of the algorithm. The challenge is due to the fact that the application of matrix exponentials are computationally expensive. Gauss elimination requires and approximate solution for a sparse matrix via conjugate gradient descent.
