Quantum Circuits Reduce Model Parameters by Nearly 16 Percent

Mateusz Papierz and colleagues at Laboratory for Advanced Materials Processing present a hybrid quantum-classical Fourier Neural Operator, termed HQ-LP-FNO, designed to improve the efficiency of surrogate modelling for three-dimensional problems. The new approach reduces the number of trainable parameters by 15.6% compared to classical methods while simultaneously enhancing accuracy, demonstrated by a 26% reduction in phase-fraction error and a decrease in relative temperature error from 2.89% to 2.56% in simulations of high-energy laser processing. The research provides a framework for evaluating hybrid quantum operator learning and confirms the numerical stability of the quantum component, suggesting a pathway towards more efficient and accurate modelling of complex multiphysics phenomena.

Hybrid quantum-classical modelling sharply enhances high-energy laser process simulation

A 10.7% improvement in accuracy has been achieved in high-energy laser processing simulations, reducing the relative temperature mean absolute error to 2.56% with a new hybrid quantum-classical approach. Traditional classical models previously yielded an error rate of 2.89%, hindering real-time control due to the computational demands of accurate three-dimensional modelling. High-energy laser processing, used in applications such as materials manufacturing and precision engineering, requires precise control of laser parameters to achieve desired material modifications. Accurate simulation of this process is computationally intensive, demanding significant resources and time, particularly when considering the complex interplay of thermal, optical, and material properties in three dimensions. HQ-LP-FNO, a novel technique developed at the Laboratory for Advanced Materials Processing, decreases the number of parameters required for these simulations by 15.6% compared to conventional methods.

The technique utilises a variational quantum circuit mixer to streamline calculations, enhancing both efficiency and predictive accuracy, with phase-fraction mean absolute error lowered by 26%. Variational quantum circuits (VQCs) are hybrid quantum-classical algorithms where a quantum circuit with adjustable parameters is optimised using a classical optimisation loop. In this context, the VQC acts as a mixer within the Fourier Neural Operator, processing spectral information more efficiently than traditional dense layer approaches. The phase-fraction error, a critical metric in laser processing simulations, represents the discrepancy between the predicted and actual phase distribution of the laser beam within the material. Reducing this error is crucial for accurate prediction of material ablation and melting. Performance gains were further validated using a noise simulation on the ibm-torino backend, confirming the numerical stability of the quantum mixer across a tested range of computational ‘shots’. ‘Shots’ refer to the number of times a quantum circuit is executed to obtain a statistical distribution of results; higher shot counts generally yield more accurate results but increase computational cost. The ibm-torino backend is a superconducting quantum computer, and demonstrating stability on such a platform is a vital step towards practical implementation. Mode-shared mixing, inherent in the variational quantum circuit’s compact structure, proved to be the primary driver of the observed improvements in accuracy. This mode-shared mixing allows for a more efficient representation of the spectral information, reducing redundancy and improving the signal-to-noise ratio. The team also designed a classical control mechanism, a parameter-matched bottleneck, to rigorously isolate the benefits of the quantum component and confirm the 15.6% reduction in trainable parameters. This bottleneck ensures that any observed improvements are directly attributable to the quantum mixer and not to changes in the classical components of the model. Currently, these results rely on simulated quantum data and do not yet demonstrate performance on actual quantum computing hardware at scale, necessitating future work on hardware implementation.

Surrogate models are increasingly vital for accelerating complex simulations, offering a cost-effective alternative to traditional multiphysics solvers. These solvers, while highly accurate, often require excessive computational resources, limiting their applicability to real-time control and optimisation tasks. Surrogate models, trained on data generated by these high-fidelity solvers, can provide accurate predictions with significantly reduced computational cost. The sheer scale of three-dimensional problems presents a persistent bottleneck, particularly concerning the number of parameters needed for accurate Fourier Neural Operators. Fourier Neural Operators (FNOs) are a class of neural networks specifically designed to solve parametric partial differential equations (PDEs). They operate in the frequency domain, allowing them to capture long-range dependencies and efficiently represent complex physical phenomena. However, the number of parameters in FNOs grows rapidly with the number of retained Fourier modes, making them computationally expensive for high-resolution three-dimensional simulations. Despite the current substantial computational demands of the quantum component, requiring significant circuit evaluations per simulation, the 15.6% reduction in parameters alongside improved accuracy demonstrates a valuable trade-off. The computational cost of the quantum component stems from the need to repeatedly evaluate the quantum circuit during the training process, a challenge that will need to be addressed through algorithmic improvements and advancements in quantum hardware.

HQ-LP-FNO successfully integrates quantum computing into Fourier Neural Operators, a type of machine learning model used to simplify complex physical systems, establishing a clear path towards more efficient simulations. The integration of quantum computing leverages the principles of quantum mechanics, such as superposition and entanglement, to potentially accelerate certain computational tasks. By employing a variational quantum circuit mixer, it reduces the number of parameters needed for accurate three-dimensional modelling of high-energy laser processing by 15.6% compared to traditional approaches. This parameter reduction is particularly significant as it directly translates to lower memory requirements and faster training times. Furthermore, a reduction in parameters can also improve the generalisation ability of the model, reducing the risk of overfitting to the training data. This parameter reduction, alongside improved accuracy in predicting material behaviour, establishes a framework for evaluating how quantum computing can enhance surrogate models. The framework developed in this research can be extended to other complex physical simulations, such as fluid dynamics, structural mechanics, and electromagnetic wave propagation. Further investigation will focus on extending this approach to other complex physical simulations, exploring different quantum circuit architectures, and investigating the potential for hardware acceleration on larger and more powerful quantum computers. The ultimate goal is to develop a fully functional quantum-enhanced surrogate modelling pipeline that can significantly accelerate the design and optimisation of complex engineering systems.

HQ-LP-FNO successfully reduced the number of trainable parameters by 15.6% when modelling three-dimensional high-energy laser processing, while simultaneously lowering phase-fraction mean absolute error by 26% and relative temperature MAE to 2.56%. This demonstrates that integrating a variational quantum circuit mixer into Fourier Neural Operators offers a valuable trade-off between model size and accuracy. Researchers established a framework for evaluating classical-quantum partitioning in surrogate models, revealing that a moderate allocation of quantum channels yields the best results. Future work will explore extending this approach to other complex physical simulations and investigating hardware acceleration.