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.
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.
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.
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.
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.
In this paper, authors present a physics-informed neural networks (PINN) approach for solving the optimal control problem (OCP) of the stochastic Schrödinger equation (SSE), with an emphasis on applications in quantum optics. The SSE models quantum systems under uncertainty, a scenario often encountered in open quantum systems where environmental interactions introduce randomness into the system dynamics. These stochastic dynamics are particularly relevant in quantum optics, where precise control over quantum states is crucial for applications such as quantum computing, secure communication, and measurement protocols. Traditional numerical methods for solving such problems face limitations due to high computational costs and the complexity associated with stochastic partial differential equations. The proposed approach utilises PINN, a type of deep learning model that integrates physical laws directly into the learning process by incorporating loss functions based on governing equations, initial and boundary conditions. The fidelity-based objective function is constructed to achieve the desired quantum state so as to develop an OCP solving algorithm. The proposed work is distinguished between deterministic drift-based training and post-training stochastic validation. Extensive numerical experiments are demonstrated near-unity deterministic fidelity. Further, a systematic architecture study validated that a moderately deep network yielded optimal performance with reduced computational cost. Fidelity dissipation analysis confirmed that the method maintained accuracy even under strong damping. These findings established the PINN as an efficient and physically consistent framework for quantum optimal control in open systems.
Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating quantum mechanical constraints via adaptive weighting, a residual-and-attention-enhanced architecture, and differentiable Cholesky parameterization for physical validity. Evaluations on 2--5 qubit systems and arbitrary-dimensional states show PINN consistently outperforms traditional neural networks (TNNs), achieving highest fidelity across all dimensions. PINN outperforms baselines, with marked improvements in moderately high-dimensional systems, superior noise robustness (slower performance degradation), and consistent dimensional robustness. Theoretical analysis shows physical constraints reduce Rademacher complexity and mitigate the curse of dimensionality via constraint-induced dimension and sample complexity reduction, effective regardless of qubit number. While experiments are limited to 5-qubit systems due to computational constraints, our theoretical framework (convergence guarantees, generalization bounds, scalability theorems) justifies PINN's advantages will persist and strengthen in larger systems (6+ qubits), where constraint-induced dimension reduction benefits grow with system size. Practically, this advances quantum error correction and gate calibration by reducing measurement requirements from O(4^n) to O(2^n) while maintaining high fidelity, enabling faster error correction cycles and accelerated calibration critical for scalable quantum computing.
Achieving scalable quantum computing demands high-fidelity operations capable of mitigating population leakage into non-computational states. Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful paradigm to unify quantum hardware characterization (inverse problems) and pulse engineering (direct problems), laying the foundational architecture for autonomous quantum processors. However, standard PINN frameworks face severe numerical bottlenecks, such as spectral bias, when attempting to simultaneously solve highly oscillatory multi-level dynamics and optimize continuous control fields under strict global phase constraints. In this work, we propose an enhanced PINN scheme for quantum optimal control (PINNQOC) that circumvents these limitations by incorporating Fourier feature embeddings, dynamic epoch normalization, and an informed pre-training routine. To rigorously evaluate its performance, we systematically benchmark our framework against two premier continuous control solvers: the first-order Krotov method and the second-order Projection Operator Newton Method for Trajectory Optimization (PRONTO). These techniques are applied to implement multiple quantum gates on a truncated three-level fluxonium qubit and a four-level Nitrogen-Vacancy center coupled to a Carbon-13 nuclear spin. Our advanced PINNQOC approach successfully suppresses population leakage while achieving gate fidelities exceeding 99.9%, matching the efficacy of traditional solvers. Finally, we provide a comprehensive analysis of computational times, iteration efficiency, and mean leakage, highlighting the distinct trade-offs and avenues for embedding physics-guided machine learning into automated quantum hardware pipelines.