Simplified experimental scheme of quantum algorithm for solving linear equations with single photons

Linear equations play an important role in nearly all fields of research in science and engineering. Recent studies have shown that quantum algorithms for solving linear systems of algebraic equations provide exponential speedups over their classical counterparts. Here, we present a simplified experimental scheme for implementing the quantum algorithm for solving linear equations with multiple degrees of freedom (DoF) of single photon. Compared with the previous studies, our scheme not only presents excellent efficiency, it requires fewer photons to solve the same problem. Our work highlights the potential applications of multiple DoFs of single photon in quantum information processes.