  The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a
quantum computational framework for solving quantum or classical optimization
tasks. Here, we explore using QAOA for Binary Linear Least Squares (BLLS); a
problem that can serve as a building block of several other hard problems in
linear algebra, such as the Non-negative Binary Matrix Factorization (NBMF) and
other variants of the Non-negative Matrix Factorization (NMF) problem. Most of
the previous efforts in quantum computing for solving these problems were done
using the quantum annealing paradigm. For the scope of this work, our
experiments were done on noiseless quantum simulators, a simulator including a
device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the
possibilities of using QAOA and QAOA-like variational algorithms for solving
such problems, where trial solutions can be obtained directly as samples,
rather than being amplitude-encoded in the quantum wavefunction. Our numerics
show that Simulated Annealing can outperform QAOA for BLLS at a QAOA depth of
$p\leq3$ for the probability of sampling the ground state. Finally, we point
out some of the challenges involved in current-day experimental implementations
of this technique on cloud-based quantum computers.
