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IEEE Communications Magazine

Physics-Informed Neural Networks for Quantum Internet Modeling: Concepts, Implementation, and Future Directions

Abdulmohsen A. Alsaui, Sunish Kumar Orappanpara Soman, B. D. E. McNiven, Hyundong Shin, Octavia A. Dobre

Published Dec 11, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1109/mcom.001.2500328

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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.
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.
Quantum communications is a promising technology that will play a fundamental role in the design of future networks. In fact, significant efforts are being dedicated by both the quantum physics and the classical communications communities on developing new architectures, solutions, and practical implementations of quantum communication networks (QCNs). Although these efforts led to various advances in today's technologies, there still exists a non-trivial gap between the research efforts of the two communities on designing and optimizing the performance of QCNs. For instance, most prior works by the classical communications community ignore important quantum physics-based constraints when designing QCNs. For example, many existing works on entanglement distribution do not account for the decoherence of qubits inside quantum memories and, thus, their designs become impractical since they assume an infinite lifetime of quantum states. In this paper, we bring forth a novel analysis of the performance of QCNs in a physics-informed manner, by relying on the quantum physics principles that underly the different components of QCNs. The need of the physics-informed approach is then assessed and its fundamental role in designing practical QCNs is analyzed across various open research areas. Moreover, we identify novel physics-informed performance metrics and controls that enable QCNs to leverage the state-of-the-art advancements in quantum technologies to enhance their performance. Finally, we analyze multiple pressing challenges and open research directions in QCNs that must be treated using a physics-informed approach to lead practically viable results. Ultimately, this work attempts to bridge the gap between the classical communications and the quantum physics communities in the area of QCNs to foster the development of the future communication networks towards the quantum Internet.
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.
Quantum communications is a promising technology that will play a fundamental role in the design of future networks. In fact, significant efforts are being undertaken by both the quantum physics and the classical communications communities on developing new architectures, solutions, and practical implementations of quantum communication networks (QCNs). Although these efforts led to various advances in today's technologies, there still exists a non-trivial gap between the research efforts of the two communities on designing and optimizing the performance of QCNs. For instance, most prior works by the classical communications community ignore important quantum physics-based constraints when designing QCNs. For example, many existing works on entanglement distribution do not account for the decoherence of qubits inside quantum memories and, thus, their designs become impractical since they assume an infinite lifetime of quantum states. In this article, we bring forth a novel analysis of the performance of QCNs in a physics-informed manner, by relying on the quantum physics principles that underly the different components of QCNs. The need for the physics-informed approach is then assessed and its fundamental role in designing practical QCNs is analyzed across various open research areas. Moreover, we identify novel physics-informed performance metrics and controls that enable QCNs to leverage the state-of-theart advancements in quantum technologies to enhance their performance. Finally, we analyze multiple pressing challenges and open research directions in QCNs that must be treated using a physics-informed approach to lead practically viable results. Ultimately, this work attempts to bridge the gap between the classical communications and the quantum physics communities in the area of QCNs to foster the development of the future communication networks toward the quantum Internet.
Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems. Here, we present a hybrid quantum-classical framework that enhances Quantum PINNs (QPINNs) through adaptive collocation point sampling and loss-aware attention mechanisms. By dynamically prioritizing points in regions with large PDE residuals or steep solution gradients, our method mitigates the spectral bias inherent in conventional PINNs. Current Quantum Physics-Informed Neural Networks are commonly assumed to be limited by the expressive power of quantum circuits. In our work, we observed that, across diverse differential equations, optimization - not only expressivity - can be an important bottleneck. Furthermore, a trainable loss-weighting scheme balances contributions from physics residuals, boundary conditions, and data fidelity during training. Integrating these strategies with quantum computing techniques (including variational quantum circuits and quantum gradient estimation) can yield at least a 60% improvement in solution accuracy under specific regimes for benchmark fluid flows and reaction-diffusion systems. Finally, we argue that merely increasing model expressivity is insufficient for resolving complex PDEs via QPINNs, as they remain constrained by the structural optimization limitations of classical PINNs. This framework provides a scalable pathway for quantum-enhanced scientific machine learning, bridging physics-based modeling with emerging quantum computational capabilities.
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.