  With the increasing popularity of quantum computing and in particular quantum
annealing, there has been growing research to evaluate the meta-heuristic for
various problems in linear algebra: from linear least squares to matrix and
tensor factorization. At the core of this effort is to evaluate quantum
annealing for solving linear least squares and linear systems of equations. In
this work, we focus on the viability of using quantum annealing for solving
these problems. We use simulations based on the adiabatic principle to provide
new insights for previously observed phenomena with the D-wave machines, such
as quantum annealing being robust against ill-conditioned systems of equations
and scaling quite well against the number of rows in a system. We then propose
a hybrid approach which uses a quantum annealer to provide a initial guess of
the solution $x_0$, which would then be iteratively improved with classical
fixed point iteration methods.
