Engineering topological states and quantum-inspired information processing using classical circuits

Abstract: Based on the correspondence between circuit Laplacian and Schrodinger equation, recent investigations have shown that classical electric circuits can be used to simulate various topological physics and the Schrodinger's equation. Furthermore, a series of quantum-inspired information processing have been implemented by using classical electric circuit networks. In this review, we begin by analyzing the similarity between circuit Laplacian and lattice Hamiltonian, introducing topological physics based on classical circuits. Subsequently, we provide reviews of the research progress in quantum-inspired information processing based on the electric circuit, including discussions of topological quantum computing with classical circuits, quantum walk based on classical circuits, quantum combinational logics based on classical circuits, electric-circuit realization of fast quantum search, implementing unitary transforms and so on.