Characterizing the interactions between quantum systems and their environment is a major limitation to the development of robust quantum technologies. In this article, the dynamics of the qubit are analyzed under the influence of two quantum noise channels, the amplitude damping channel and the pure dephasing channel. We evaluate their respective and combined impact on the quantum state and the evolution of populations and coherence over time. we also present a comprehensive framework for performing Lindblad equation using Physics-Informed Neural Networks (PINNs). Our approach relies on learning the Lindblad equation to simulate the evolution of the quantum state under quantum noise channels. Our results demonstrate that PINN model can reproduce the dynamics of the quantum system, thus offering an efficient modeling of open quantum systems.
Characterizing the interactions between quantum systems and their environment is a major limitation to the development of robust quantum technologies. In this article, the dynamics of the qubit are analyzed under the influence of two quantum noise channels, the amplitude damping channel and the pure dephasing channel. We evaluate their respective and combined impact on the quantum state and the evolution of populations and coherence over time. we also present a comprehensive framework for performing Lindblad equation using Physics-Informed Neural Networks (PINNs). Our approach relies on learning the Lindblad equation to simulate the evolution of the quantum state under quantum noise channels. Our results demonstrate that PINN model can reproduce the dynamics of the quantum system, thus offering an efficient modeling of open quantum systems.
Characterizing the environmental interactions of quantum systems is a critical bottleneck in the development of robust quantum technologies. Traditional tomographic methods are often data-intensive and struggle with scalability. In this work, we introduce a novel framework for performing Lindblad tomography using Physics-Informed Neural Networks (PINNs). By embedding the Lindblad master equation directly into the neural network's loss function, our approach simultaneously learns the quantum state's evolution and infers the underlying dissipation parameters from sparse, time-series measurement data. Our results show that PINNs can reconstruct both the system dynamics and the functional form of unknown noise parameters, presenting a sample-efficient and scalable solution for quantum device characterization. Ultimately, our method produces a fully-differentiable digital twin of a noisy quantum system by learning its governing master equation.
The classical Internet faces increasing limitations as data generation and device interconnectivity expand at unprecedented rates. In recent years, this has highlighted the need for communication frameworks that surpass classical limitations. The quantum Internet (QI), composed of multiple layers of quantum communication networks (QCNs), holds promise for remarkable capabilities in secure transmission, distributed quantum computing, and quantum-enhanced sensing. Accurate and scalable modeling of QCNs is essential for designing, analyzing, and optimizing QI protocols under realistic physical conditions. To model such open quantum systems under Markovian noise, the Lindblad master equation is widely used, but its modeling complexity grows exponentially with the system size. In this work, we introduce a learned approach that utilizes a physics-informed neural network (PINN) to model the dynamics of open quantum systems, which embeds the Lindblad formalism directly into the neural network's loss function. We demonstrate the effectiveness of our method by simulating the entanglement fidelity decay of a two-qubit Bell state under energy damping and phase decoherence noise, which is a relevant scenario for entanglement-based QI protocols. Preliminary numerical results show that the PINN-based solver aligns with conventional partial differential equation techniques while offering improved scalability. These findings suggest that PINNs could serve as an efficient approach for accelerating the analysis of future quantum networking solutions. Finally, we conclude by outlining key future directions for scaling the framework to support QCN-level optimization.
Quantum systems in near-term devices operate in noisy, open-system regimes where decoherence and control imperfections are unavoidable. This study presents a physics-informed neural-network framework for modelling, noiseaware simulation, and residual-based control of open quantum systems, validated against a closed-form Lindblad solution for a driven, amplitude-damped qubit rather than a numerical reference. Across three random seeds, the trained network reproduces population and coherence dynamics with a mean RMSE of 0.00060 and a standard deviation of 0.00054. The mixed-state fidelity exceeds 0.999999 over the evaluation trajectory, while the squared Bloch-vector norm remains within the physical bound for the main modelling benchmark. Removing the Fourier-feature input encoding produces a 70-fold degradation in RMSE, confirming a strong representational benefit for the oscillatory dynamics. Direct comparison against fourth-order Runge-Kutta integration shows the classical solver to be approximately five orders of magnitude faster and two orders more accurate at this scale; the value of the proposed framework for a single qubit therefore lies in data-free, physics-constrained modelling rather than computational speed. A residual-based state-transfer control demonstration and a control-effort sweep further reveal a clear fidelity-versus-energy trade-off and a marked reduction in seed-to-seed variation as regularisation increases. These results support physics-constrained learning as a faithful approach to singlequbit open-system modelling and control, while motivating further validation on multi-qubit systems before broader scalability claims are made.
Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their usefulness in predicting such pulses. Our PINN is a feedforward neural network that utilizes an unsupervised learning approach, whose loss function includes terms that enforce the equations that govern the evolution of a quantum system, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We use a sinusoidal activation function and adopt variance-type weight initialization, tailored to our activation function. By analyzing the model's performance with important machine learning metrics, we demonstrate that the choice of our architecture is well-suited for this type of problem. We ensure that our network avoids the vanishing and exploding gradients with our relevant choices. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness.
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.
Abstract We demonstrate that system-agnostic physics-informed neural networks (PINNs) can efficiently learn the dynamical solution of quantum master equations, as compared to problem-specific numerical solvers, with respect to accuracy, stability of training convergence, robustness towards bath parameters or initial conditions, and equivalent convergence times for the non-Markovian evolution of two-level quantum systems. We study cases of quantum dot systems driven by external electromagnetic fields and coupled to an acoustic phonon environment, and analyze two problem setups, the evolution of Bloch vectorized coupled differential equations obtained from a Lindblad master equation and the evolution of a non-Markovian master equation obtained from the Nakajima–Zwanzig formulation. We implement a fully connected PINN architecture to solve the two problems. We also use the same methodology to solve the inverse problem of estimation of bath parameters in a supervised fashion, but with a very limited number of noisy samples.