Investigations reveal how a quantum kernel impacts active learning when using Gaussian Process Regression (GPR). The framework’s performance relies keyly on selecting an appropriate surrogate model. With Gaussian Process Regression (GPR) as the surrogate, its effectiveness is largely determined by the expressivity of the underlying kernel. This study focuses on sensitivity to regularisation through hyperparameter tuning. Empirical evidence shows that even at small scales, overfitting can compromise GPR performance, although generic unstructured kernels suffer from exponential concentration at large scale. Kernel regularisation enables mitigation of this effect because of observed smoothness.

Kernel regularisation enables strong Gaussian process regression with expressive quantum kernels

Mean squared error decreased to 0.23 through kernel regularization, representing an almost forty per cent improvement over unregularized quantum kernels. Previously, those kernels exhibited rapid performance collapse at small scales and prevented reliable Gaussian Process Regression modelling of black-box functions within active learning frameworks when data points were limited. Careful hyperparameter tuning, adjusting signal variance and noise levels specifically, effectively balances the benefits of these powerful kernels alongside the need for generalisation.

Signal variance adjustments up to 10 percent improved predictive accuracy by preventing overconfidence in the Gaussian Process Regression surrogate model during active learning. These findings are particularly relevant because they allow incorporation of realistic noise from near-term quantum devices into training processes, improving overall model durability. This approach successfully transferred across different restricted quantum kernels designed for efficient computation while avoiding exponential concentration issues common with high dimensional models. However, results stemmed from a one-dimensional black-box function; scaling this framework to more complex multidimensional problems remains an open challenge hindering immediate practical application.

Quantum Kernel Regularisation Mitigates Overfitting in Limited Data Scenarios

Surrogate models are increasingly relied upon to navigate computationally expensive problems within fields like engineering and drug discovery. Gaussian Process Regression (GPR), a powerful technique for building these surrogates, critically hinges on the kernel used to define similarity between data points. Quantum kernels offer potential advantages by mapping inputs into complex high-dimensional spaces but achieving strong performance requires careful hyperparameter tuning to prevent overfitting even when dealing with limited datasets.

The difficulty of fine-tuning quantum kernels should not overshadow their value; gains in modelling complex systems remain significant given the cost of initial data generation. Adjusting how much emphasis is placed on smooth versus flexible models through kernel regularization is important for success with this approach. Effective performance necessitates balancing expressive power against the risk of overfitting, where models excel at training data yet perform poorly with new information and moves beyond simply demonstrating functionality by clarifying practical deployment strategies even with real-world scientific applications’ commonly limited datasets.

The research demonstrated that using a quantum kernel alongside Gaussian Process Regression requires careful adjustment to prevent overfitting, particularly when working with small amounts of data. This matters because surrogate modelling relies on accurately representing complex systems from limited initial measurements, as is common in areas like engineering and drug discovery. Researchers found that incorporating realistic noise, mirroring limitations of current quantum devices, improved model robustness across different restricted kernels. The study focused on a one-dimensional problem, suggesting further work is needed to extend this framework to more complicated scenarios.

👉 More information
🗞 Balancing Expressivity and Overfitting in Quantum Gaussian Process Regression
✍️ Saasha Joshi, Udson C. Mendes and Luke C. G. Govia
🧠 ArXiv: https://arxiv.org/abs/2609.09407

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