  Multiple linear regression assumes an imperative role in supervised machine
learning. In 2009, Harrow et al. [Phys. Rev. Lett. 103, 150502 (2009)] showed
that their HHL algorithm can be used to sample the solution of a linear system
$\mathbf{Ax=b}$ exponentially faster than any existing classical algorithm,
with some manageable caveats. The entire field of quantum machine learning
gained considerable traction after the discovery of this celebrated algorithm.
However, effective practical applications and experimental implementations of
HHL are still sparse in the literature. Here, we demonstrate a potential
practical utility of HHL, in the context of regression analysis, using the
remarkable fact that there exists a natural reduction of any multiple linear
regression problem to an equivalent linear systems problem. We put forward a
$7$-qubit quantum circuit design, motivated from an earlier work by Cao et al.
[Mol. Phys. 110, 1675 (2012)], to solve a $3$-variable regression problem,
using only elementary quantum gates. We also implement the Group Leaders
Optimization Algorithm (GLOA) [Mol. Phys. 109 (5), 761 (2011)] and elaborate on
the advantages of using such stochastic algorithms in creating low-cost circuit
approximations for the Hamiltonian simulation. We believe that this application
of GLOA and similar stochastic algorithms in circuit approximation will boost
time- and cost-efficient circuit designing for various quantum machine learning
protocols. Further, we discuss our Qiskit simulation and explore certain
generalizations to the circuit design.
