Diffusion-based Quantum Error Mitigation using Stochastic Differential Equation

Unlike closed systems, where the total energy and information are conserved within the system, open systems interact with the external environment which often leads to complex behaviors not seen in closed systems. The random fluctuations that arise due to the interaction with the external environment cause noise affecting the states of the quantum system, resulting in system errors. To effectively concern quantum error in open quantum systems, this paper introduces a novel approach to mitigate errors using diffusion models. This approach can be realized by noise occurrence formulation during the state evolution as forward-backward stochastic differential equations (FBSDE) and adapting the score-based generative model (SGM) to denoise errors in quantum states.