Adaptive Conformal Prediction for Quantum Machine Learning

TL;DR

This work tackles uncertainty quantification in quantum machine learning under time-varying hardware noise, which breaks the exchangeability assumptions behind standard conformal prediction. It introduces Adaptive Quantum Conformal Prediction (AQCP), an adaptation of Adaptive Conformal Inference that performs online recalibration to maintain target coverage $1-\alpha$ despite drift. The authors formalize how non-stationary noise undermines exchangeability, prove asymptotic average coverage guarantees for AQCP, and validate the approach with experiments on IBM quantum hardware, comparing several score functions. Results show AQCP achieves target coverage with greater stability than prior quantum conformal prediction, providing a practical framework for reliable uncertainty quantification in NISQ-era quantum learning.

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 user-specified 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.

Figures (5)

• Figure 1: Diagrams of three entangling-block configurations within a four-qubit circuit implemented using CZ gates: (a) a linear entangling block, (b) a circular entangling block, and (c) a full entangling block.
• Figure 2: Regression Model Shots (Simulated vs. ibm_sherbrooke). Comparison of $100{,}000$ shots sampled from each backend (Qiskit Aer simulator and ibm_sherbrooke). The marker size is scaled proportionally to the count of overlapping shots at each location. The red lines represent the component mean functions $\mu(x)$ and $-\mu(x)$.
• Figure 3:
• Figure 4:
• Figure 5: Average coverage and average set size of AQCP ($\gamma = 0.03$), evaluated across a range of shot numbers $M$ using shot data from $\mathtt{FakeQuitoV2}$. The desired miscoverage is set to $\alpha=0.1$. Averages are computed from prediction sets returned from Algorithm \ref{['alg:AQCP_batch_predict']} with $100$ initial calibration points and $9{,}900$ test points. (a) Average prediction set size for a range of score functions. (b) Corresponding average coverage for the same score functions. The optimal line represents the performance of the benchmark ${\mathcal{C}}^*$ family of prediction sets.

Theorems & Definitions (5)

• Theorem 1: vovk2005algorithmiclei2017distributionfree
• Theorem 2: Finite Sample Guarantee for AQCP, Adapted from ACI
• Theorem 3
• Theorem 4
• Lemma 1