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.
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.
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.
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.
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 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.
Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource efficiency, especially under limited measurements. In this work, we present Inverse Physics-Informed Neural Networks for Hamiltonian Learning (iPINN-HL), an approach that incorporates the Schrödinger equation as a soft constraint via a loss function penalty into the ML procedure. This formulation allows the model to integrate both observational data and known physical laws to infer Hamiltonian parameters with greater accuracy and resource efficiency. We benchmark iPINN-HL against a deep-neural-network-based quantum state tomography method [denoted as DNN-HL (Deep Neural Network for Hamiltonian Learning)] and demonstrate its effectiveness across several different scenarios, including one-dimensional spin chains, cross-resonance gate calibration, crosstalk identification, and real-time compensation to parameter drift. Our results show that iPINN-HL can approach the Heisenberg limit and exhibits robustness to noises, while outperforming DNN-HL in accuracy and resource efficiency. Therefore, iPINN-HL is a powerful and flexible framework for quantum system characterization for practical tasks.
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.