Equation-Free Discovery of Open Quantum Systems via Paraconsistent Neural Networks

TL;DR

This paper introduces ParaQNN, a novel equation-free neural network architecture using paraconsistent logic to discover and model the dynamics of open quantum systems from noisy data, outperforming traditional methods especially in extrapolation.

Contribution

The paper presents ParaQNN, a new physics-discovery neural network that employs paraconsistent logic to model quantum dynamics without predefined equations, enabling better generalization and discovery in noisy, complex regimes.

Findings

ParaQNN outperforms RF, XGBoost, and PINN in benchmark tests.

It maintains accuracy in extrapolation regions with noisy data.

Successfully models complex mixed quantum regimes.

Abstract

Modeling the dynamics of open quantum systems on noisy intermediate-scale quantum (NISQ) devices constitutes a major challenge, as high noise levels and environmental degradations lead to the decay of pure quantum states (decoherence) and energy losses. This situation represents one of the most important problems in the field of quantum information technologies. While existing data-driven methods struggle to generalize beyond the training data (extrapolation), physics-informed neural networks (PINNs) require predefined governing equations, which limit their discovery capability when the underlying physics is incomplete or unknown. In this work, we present the ParaQNN (ParaQuantum neural network) architecture, an equation-free framework for physical discovery. ParaQNN disentangles multi-scale dynamics without relying on a priori laws by employing a dialetheist logic layer that models coherent signal and decoherent noise as independent yet interacting channels. Through extensive benchmark tests performed on Rabi oscillations, Lindblad dynamics, and particularly complex "mixed regimes" where relaxation and dephasing processes compete, we show that ParaQNN exhibits a consistent performance advantage compared to Random Forest, XGBoost, and PINN models with incomplete physical information. Unlike its competitors, ParaQNN succeeds in maintaining oscillatory and damping dynamics with high accuracy even in extrapolation regions where training data are unavailable, by "discovering" the underlying structural invariants from noisy measurements. These results demonstrate that paraconsistent logic provides a structurally more stable epistemic foundation than classical methods for learning quantum behavior in situations where mathematical equations prove insufficient.