Quantum Convolutional Neural Networks for Groundwater Heat Plume Prediction: A Surrogate Modeling Approach

Research Context and Objective

Predicting groundwater temperature variations induced by geothermal heat pumps is essential for urban planning and environmental protection, particularly in cities like Munich. While high-fidelity numerical simulations (e.g., using Pflotran) are accurate, they are computationally expensive and unsuitable for real-time applications or large-scale scenario modeling. This study investigates the use of Quantum Convolutional Neural Networks (QCNNs) as a surrogate model to predict heat plume characteristics—such as length, width, and maximum temperature—based on subsurface permeability and pressure gradients.

To address the scalability limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, the authors reduced high-dimensional simulation outputs into a compact set of representative parameters. The QCNN architecture consists of three main components: a quantum convolutional layer for feature extraction, a quantum pooling layer for dimensionality reduction, and a fully connected quantum readout stage. The model utilizes an Instantaneous Quantum Polynomial (IQP) encoding scheme to map classical input data into quantum states. The researchers benchmarked the model across multiple backends, including ideal statevector simulators, noisy simulators, and IBM’s 127-qubit Kyiv quantum processor, both with and without advanced error-mitigation strategies.

Findings and Significance

The results demonstrate that QCNNs are capable of learning the underlying dynamics of groundwater heat plumes. Although classical neural networks currently achieve higher predictive accuracy, the QCNN exhibits competitive performance on simulators. Notably, the application of error-mitigation techniques on physical hardware leads to a measurable improvement in prediction quality. This work highlights that quantum-enhanced surrogate modeling is a viable, evolving path for environmental modeling, suggesting that as quantum hardware matures and error-mitigation protocols become more sophisticated, these models may eventually bridge the gap between computational speed and simulation accuracy.