Authors:

Purav Matlia

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About Paper:

In many scientific and engineering domains, operators-mappings between infinite-dimensional function spaces-are used to model functional relationships, including those arising in the solution of partial differential equations (PDEs). Deep Operator Networks (DeepONets) offer a data-driven framework for learning such operators, but classical DeepONets face challenges related to computational scalability and reliable uncertainty quantification, particularly during rare but critical events. To address these issues, we build on recent advances in quantum machine learning by extending the quantum DeepONet framework, which reduces forward-pass complexity from quadratic to linear. We incorporate the Superposed Parameterized Quantum Circuit (SPQC) architecture to represent an ensemble of quantum DeepONets within a single parameterized quantum circuit. The ensemble is constructed using random initialization and bootstrap aggregation (bagging), and the SPQC enables the simultaneous evaluation of all ensemble members in one quantum inference pass. To support reliable uncertainty estimates, we use a conformal prediction framework that generates prediction intervals with guaranteed accuracy. We evaluate our approach using the antiderivative operator and analyze the impact of quantum measurement noise on predictive reliability. Our results demonstrate that this method enables scalable operator learning on fault-tolerant future hardware while supporting rigorous uncertainty estimation, making it a promising approach for real-time, high-stakes applications such as power system monitoring. Keywords: Quantum Machine Learning; Operator Learning; Uncertainty Quantification; Conformal Prediction; Deep Operator Network (DeepONet)

Source:

Purdue University / 2025

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Co-authors:

Purav Matlia