Adaptive Conformal Prediction for Quantum Machine Learning

TMLR Paper6789 Authors

Abstract: Quantum machine learning seeks to leverage quantum computers to improve upon classical machine learning algorithms. Currently, robust uncertainty quantification methods remain underdeveloped in the quantum domain, despite the critical need for reliable and trustworthy predictions. Recent work has introduced quantum conformal prediction, a framework that produces prediction sets that are guaranteed to contain the true outcome with userspecified probability. In this work, we formalise how the time-varying noise inherent in quantum processors can undermine conformal guarantees, even when calibration and test data are exchangeable. To address this challenge, we draw on Adaptive Conformal Inference, a method which maintains validity over time via repeated recalibration. We introduce Adaptive Quantum Conformal Prediction (AQCP), an algorithm which preserves asymptotic average coverage guarantees under arbitrary hardware noise conditions. Empirical studies on an IBM quantum processor demonstrate that AQCP achieves target coverage levels and exhibits greater stability than quantum conformal prediction.

Submission Type: Long submission (more than 12 pages of main content)

Changes Since Last Submission:

We thank the reviewers for their thoughtful and constructive feedback. The main changes since the last submission are summarised below.

(1) Expanded discussions for greater transparency.

We renamed the AQCP Implementation section to Algorithm Implementation and Evaluation Strategy and expanded it to more clearly justify our evaluation choices and experimental protocol.

We added a new Limitations and Future Work section to more clearly articulate the scope of our results, practical constraints of the current approach, and promising directions for future research.

We also added a new appendix section, Ties to Adaptive Quantum Conformal Prediction, to explicitly clarify how the theoretical framework developed in the appendix applies to the setting studied in the main body.

(2) Improved exposition.

We refined the presentation of Theorem 2 by more carefully defining the relevant objects. These revisions do not alter the statement or validity of the theorem.

We refined the conformal prediction background section to clarify notational choice and increase clarity.

(3) Minor revisions and consistency improvements.

We added two additional references to the QML background to enrich citations.

To improve notational consistency, we renamed the score function $s_\text{Euc}(\cdot)$ to $\hat S_\text{Euc}(\cdot)$ (and similarly for other named score functions) to align with the general notation $\hat S$ used throughout the paper.

We made numerous minor formatting, and typographical, and SPAG improvements throughout the manuscript.

Assigned Action Editor: ~Jake_Snell1

Submission Number: 6789