This study introduces a quantum-accelerated framework that integrates quantum optimization with physics-informed neural networks (PINNs) to solve PDEs more efficiently. By leveraging the Quantum Approximate Optimization Algorithm (QAOA), the proposed framework enhances the initialization and boundary parameter optimization of PINNs, addressing key challenges such as slow convergence and high computational cost. The hybrid approach combines the data efficiency and physical constraint embedding capabilities of PINNs with the computational advantages of quantum optimization, enabling faster and more accurate solutions for complex PDEs. The framework was validated using the Shuhao Cao PDE dataset, demonstrating significant improvements in training efficiency and accuracy compared to traditional numerical solvers and classical PINNs. Experimental results highlight that quantum optimization effectively accelerates convergence by optimizing initial conditions and boundary constraints, reducing the computational overhead associated with classical training processes. Despite its reliance on emerging quantum hardware and the sensitivity of PINNs to hyperparameter selection, this approach offers a scalable and robust solution for solving high-dimensional PDEs. The findings underscore the potential of hybrid quantum-classical methods in advancing scientific computing, providing a foundation for future research in stochastic PDEs, multi-physics problems, and other real-world applications.
This study introduces a quantum-accelerated framework that integrates quantum optimization with physics-informed neural networks (PINNs) to solve PDEs more efficiently. By leveraging the Quantum Approximate Optimization Algorithm (QAOA), the proposed framework enhances the initialization and boundary parameter optimization of PINNs, addressing key challenges such as slow convergence and high computational cost. The hybrid approach combines the data efficiency and physical constraint embedding capabilities of PINNs with the computational advantages of quantum optimization, enabling faster and more accurate solutions for complex PDEs. The framework was validated using the Shuhao Cao PDE dataset, demonstrating significant improvements in training efficiency and accuracy compared to traditional numerical solvers and classical PINNs. Experimental results highlight that quantum optimization effectively accelerates convergence by optimizing initial conditions and boundary constraints, reducing the computational overhead associated with classical training processes. Despite its reliance on emerging quantum hardware and the sensitivity of PINNs to hyperparameter selection, this approach offers a scalable and robust solution for solving high-dimensional PDEs. The findings underscore the potential of hybrid quantum-classical methods in advancing scientific computing, providing a foundation for future research in stochastic PDEs, multi-physics problems, and other real-world applications.
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.
Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to accelerate the solution of PDEs is promising, but not competitive with numerical solvers yet. Here, we show how quantum computing can improve the ability of physics-informed neural networks to solve partial differential equations. For this, we develop hybrid networks consisting of quantum circuits combined with classical layers and systematically test them on various non linear PDEs and boundary conditions in comparison with purely classical networks. We demonstrate that the advantage of using quantum networks lies in their ability to achieve an accurate approximation of the solution in substantially fewer training epochs, particularly for more complex problems. These findings provide the basis for targeted developments of hybrid quantum neural networks with the goal to significantly accelerate numerical modeling.
Q-PINN-opt creates a new framework by combining the concepts of quantum computing with Physics-Informed Neural Networks (PINNs) for multi-modal optimization of diffractive optics under laser conditions. In high-power laser applications, which involve the optimization of complex problems, the model employs quantum-enhanced optimization coupled with physics-informed learning. In contrast to traditional approaches based on PINNs or Wiener filters, which are limited by their inability to scale, poor computational efficiency, and limited resilience to extreme conditions, Q-PINN-opt is a hybrid quantum-classical algorithm that accelerates convergence and maximizes computational efficiency. The major innovation of the Q-PINN-opt variant is that quantum algorithms (such as Quantum Gradient Descent and Quantum Approximate Optimization Algorithm (QAOA)) are implemented using classical PINNs. This enables faster, scalable, and multimodal optimization of problems, including diffraction efficiency, phase accuracy, and resistance to thermal, non-linear, and quantum-induced effects. Current models such as PINNs may also exhibit slow convergence and computational inefficiency when applied to optimization problems of complex, high-dimensional nature, especially when multiple performance criteria are to be optimized simultaneously. Q-PINN-opt addresses all these shortcomings; thus, it is specifically applicable to the optimization of diffractive optics for real-time adaptive learning. Q-PINN-opt addresses this problem by leveraging quantum computing to train more effectively and process large-scale data efficiently. Moreover, the hybrid quantum-classical model ensures the racial-physical constraints of network solutions, enhancing the resilience and scalability of high-performance optical systems. The Q- INN-opt framework metric analysis reveals that it performs better than models. MSE, SSIM, and SNR in the model are 6.84, 0.99, and 7.98, respectively, which imply the model has high accuracy, diffraction efficiency, and resistance to noise. Compared with the Original Model, the Original Model has an MSE of 9.55 and an SNR of 5.54. This improved both the training and the convergence of the optimization, making Q-PINN-opt well-constructed and efficient for the design of complicated diffractive optics in extreme environments.
Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to leverage the usage of Machine Learning computational frameworks relying on the combined usage of CPUs and co-processors, such as accelerators, to achieve maximum performance. This work investigates the design, implementation, and performance of PINNs, using the Quantum Processing Unit (QPU) co-processor. We design a simple Quantum PINN to solve the one-dimensional Poisson problem using a Continuous Variable (CV) quantum computing framework. We discuss the impact of different optimizers, PINN residual formulation, and quantum neural network depth on the quantum PINN accuracy. We show that the optimizer exploration of the training landscape in the case of quantum PINN is not as effective as in classical PINN, and basic Stochastic Gradient Descent (SGD) optimizers outperform adaptive and high-order optimizers. Finally, we highlight the difference in methods and algorithms between quantum and classical PINNs and outline future research challenges for quantum PINN development.
We present QPINNACLE, an open-source computational framework for physics-informed neural networks (PINNs) that integrates modern training strategies, multi-GPU acceleration, and hybrid quantum-classical architectures within a unified modular workflow. The framework enables systematic evaluation of PINN performance across benchmark problems including 1D hyperbolic conservation laws, incompressible flows, and electromagnetic wave propagation. It supports a range of architectural and training enhancements, including Fourier feature embeddings, random weight factorization, strict boundary condition enforcement, adaptive loss balancing, curriculum training, and second-order optimization strategies, with extensibility to additional methods. We provide a comprehensive benchmark study quantifying the impact of these methods on convergence, accuracy, and computational cost, and analyze distributed data parallel scaling in terms of runtime and memory efficiency. In addition, we extend the framework to hybrid quantum-classical PINNs and derive a formal estimate for circuit-evaluation complexity under parameter-shift differentiation. Results highlight the sensitivity of PINNs to architectural and training choices, confirm their high computational cost relative to classical solvers, and identify regimes where hybrid quantum models offer improved parameter efficiency. QPINNACLE provides a foundation for benchmarking physics-informed learning methods and guiding future developments through quantitative assessment of their trade-offs.
This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory behavior. Traditional physics-informed neural networks (PINNs) have demonstrated substantial potential in solving differential equations, and their quantum counterparts, quantum-PINNs, exhibit enhanced representational capacity with fewer trainable parameters. However, both approaches face notable challenges in accurately solving multiscale features. Furthermore, their reliance on automatic differentiation for constructing loss functions introduces considerable computational overhead, resulting in longer training times. To overcome these challenges, we developed a wavelet-accelerated physics-informed quantum neural network that eliminates the need for automatic differentiation, significantly reducing computational complexity. The proposed framework incorporates the multiresolution property of wavelets within the quantum neural network architecture, thereby enhancing the network's ability to effectively capture both local and global features of multiscale problems. Numerical experiments demonstrate that our proposed method achieves superior accuracy while requiring less than five percent of the trainable parameters compared to classical wavelet-based PINNs, resulting in faster convergence. Moreover, it offers a speedup of three to five times compared to existing quantum PINNs, highlighting the potential of the proposed approach for efficiently solving challenging multiscale and oscillatory problems.