Quantum approximate optimization for hard problems in linear algebra

The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a computational framework for solving or classical tasks. Here, we explore using QAOA binary linear least squares (BLLS); problem that can serve as building block of several other hard problems in algebra, such the non-negative matrix factorization (NBMF) and variants (NMF) problem. Most previous efforts computing these were done annealing paradigm. For scope this work, our experiments on noiseless simulators, simulator including device-realistic noise-model, two IBM Q 5-qubit machines. We highlight possibilities QAOA-like variational algorithms problems, where trial solutions be obtained directly samples, rather than being amplitude-encoded wavefunction. Our numerics show even small number steps, simulated outperform BLLS at depth p\leq3 p?3 probability sampling ground state. Finally, point out some challenges involved current-day experimental implementations technique cloud-based computers.