Quantum linear systems algorithms: a primer

Understand

The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart.

• The problem of solving a system of linear equations has a wide scope of applications, and thus HHL constitutes an important algorithmic primitive.
• In these notes, we present the HHL algorithm and its improved versions in detail, including explanations of the constituent sub- routines.
• More specifically, we discuss various quantum subroutines such as quantum phase estimation and amplitude amplification, as well as the important question of loading data into a quantum computer, via quantum RAM.