Quantum simulation of classical RCL circuits via complexification and Schrödingerization

Abstract

The decomplexification procedure establishes a mathematical equivalence between finite dimensional quantum dynamics and classical dynamics by mapping the complex quantum domain onto the real classical one. Its inverse process, complexification --- which lifts a classical dynamics to an equivalent quantum formulation --- is of great interest, particularly because it enables the quantum simulation of equations that are of classical relevance. In this way, one can prepare the solution of classical differential equations to be implemented using quantum computation tools. In the present work, we recall the decomplexification procedure and also discuss several distinct strategies for performing the complexification of classical equations, so as to obtain the corresponding quantum-equivalent dynamics.