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 even for a small
number of steps, simulated annealing can outperform QAOA for BLLS at a
QAOA depth of p\leq3p≤3
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.