  Binary Neural Networks are a promising technique for implementing efficient
deep models with reduced storage and computational requirements. The training
of these is however, still a compute-intensive problem that grows drastically
with the layer size and data input. At the core of this calculation is the
linear regression problem. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm
has gained relevance thanks to its promise of providing a quantum state
containing the solution of a linear system of equations. The solution is
encoded in superposition at the output of a quantum circuit. Although this
seems to provide the answer to the linear regression problem for the training
neural networks, it also comes with multiple, difficult-to-avoid hurdles. This
paper shows, however, that useful information can be extracted from the
quantum-mechanical implementation of HHL, and used to reduce the complexity of
finding the solution on the classical side.
