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This paper presents a system for solving binary-valued linear equations usingquantum computers. The system is called Mod2VQLS, which stands for Modulo2Variational Quantum Linear Solver. As far as we know, this is the first suchproposal. The design is a classical-quantum hybrid. The quantum components area new circuit design for implementing matrix multiplication modulo 2, and avariational circuit to be optimized. The classical components are the optimizerwhich measures the cost function and updates the quantum parameters for eachiteration, and the controller that runs the quantum job and classical optimizeriterations. We propose two alternative ansatze or templates for the variationalcircuit, and present results showing that the rotation ansatz designedspecifically for this problem provides the most direct path to a validsolution. Numerical experiments in low dimensions indicate that Mod2VQLS, usingthe custom rotations ansatz, is on-a-par with the block Wiedemann algorithm,the best-known to date for this problem.

Mod2VQLS: a Variational Quantum Algorithm for Solving Systems of Linear Equations Modulo 2