Diffusion-based Quantum Error Mitigation using Stochastic Differential Equation

TL;DR

This paper proposes a novel quantum error mitigation method for open systems using diffusion models, specifically forward-backward stochastic differential equations and score-based generative models, to reduce noise-induced errors.

Contribution

It introduces a new approach combining stochastic differential equations and generative models for quantum error mitigation in open quantum systems.

Findings

Effective noise reduction in quantum states demonstrated

Integration of FBSDE with score-based models for error correction

Potential for improved quantum system stability

Abstract

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.