Quantum Approximate Optimization for Hard Problems in Linear Algebra.

The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a framework for hybrid quantum/classical optimization. In this paper, we explore using QAOA for binary linear least squares; a problem that can serve as a building block of several other hard problems in linear algebra. 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 the QISKIT simulator and an IBM Q 5 qubit machine. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where the result outputs produced are classical. We find promising numerical results, and point out some of the challenges involved in current-day experimental implementations of this technique on a cloud-based quantum computer.