  This paper presents a system for solving binary-valued linear equations using
quantum computers. The system is called Mod2VQLS, which stands for Modulo2
Variational Quantum Linear Solver. As far as we know, this is the first such
proposal. The design is a classical-quantum hybrid. The quantum components are
a new circuit design for implementing matrix multiplication modulo 2, and a
variational circuit to be optimized. The classical components are the optimizer
which measures the cost function and updates the quantum parameters for each
iteration, and the controller that runs the quantum job and classical optimizer
iterations. We propose two alternative ansatze or templates for the variational
circuit, and present results showing that the rotation ansatz designed
specifically for this problem provides the most direct path to a valid
solution. Numerical experiments in low dimensions indicate that Mod2VQLS, using
the custom rotations ansatz, is on-a-par with the block Wiedemann algorithm,
the best-known to date for this problem.
