Engineering Topological States and Quantum-Inspired Information Processing Using Classical Circuits

Based on the correspondence between circuit Laplacian and Schrodinger equations, recent investigations have shown that classical electric circuits can be used to simulate various topological physics and Schrödinger's equation. Furthermore, a series of quantum-inspired information processing has been implemented by using classical electric circuit networks. In this review, the similarity between the circuit Laplacian and the lattice Hamiltonian is analyzed, with topological physics introduced based on classical circuits. Subsequently, reviews of the research progress in quantum-inspired information processing based on the electric circuit are provided, 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.