Adaptive Conformal Prediction Maintains Validity in Quantum Machine Learning Despite Time-varying Noise

Quantum machine learning promises to enhance existing algorithms, but a crucial challenge remains, namely the need for reliable prediction uncertainty. Douglas Spencer, Samual Nicholls, and Michele Caprio, all from the University of Oxford, address this problem by formalising how the inherent instability of quantum processors can compromise standard prediction accuracy. Their work introduces Adaptive Conformal Prediction, a novel algorithm that maintains trustworthy prediction sets even when faced with fluctuating hardware performance. The team demonstrates that this method preserves prediction accuracy over time, achieving stable and reliable results on real quantum hardware and representing a significant step towards practical, trustworthy quantum machine learning applications.

Recent work introduces quantum conformal prediction, a framework that generates prediction sets guaranteed to contain the correct outcome with a user-defined probability. However, these methods assume stable hardware, a limitation in practice. Researchers now formalise how time-varying noise undermines these guarantees, even with careful calibration and test data. To address this, they draw on Adaptive Conformal Inference, a technique that maintains validity over time through repeated recalibration, and introduce Adaptive Quantum Conformal Prediction (AQCP), a new approach built on these foundations.

Adaptive Quantum Prediction Handles Noise Online

Researchers developed Adaptive Quantum Conformal Prediction (AQCP), a novel algorithm designed to address the challenges of uncertainty quantification in quantum machine learning, particularly those arising from fluctuating noise in quantum processors. This study pioneers a method for maintaining reliable prediction sets even when hardware introduces time-varying errors, a limitation of existing quantum conformal prediction techniques. Building on Adaptive Conformal Inference, AQCP extends its principles to the quantum realm through online recalibration, a process that dynamically adjusts predictions to account for non-stationary noise. To implement AQCP, scientists leveraged parametrised quantum circuits (PQCs) and analysed their sampled measurement outcomes, mirroring the approach of Quantum Conformal Prediction.

This recalibration process involves repeatedly assessing model performance with new data, allowing the algorithm to adapt to evolving noise characteristics within the quantum processor. Experiments employed an IBM quantum processor to rigorously test AQCP’s performance, demonstrating its ability to achieve target coverage levels while maintaining greater stability than standard quantum conformal prediction. The study further investigated the impact of different score functions on prediction set size, comparing their average performance when integrated with AQCP. Researchers meticulously analysed the resulting prediction sets, evaluating their ability to reliably encompass true outcomes under varying noise conditions. This detailed analysis reveals that AQCP effectively mitigates the effects of non-stationary noise, providing a robust and trustworthy method for uncertainty quantification in quantum machine learning applications.

Adaptive Quantum Prediction Handles Processor Noise

The research team developed Adaptive Quantum Conformal Prediction (AQCP), a new algorithm designed to maintain reliable prediction accuracy even with the inherent noise present in quantum processors. This work addresses a critical limitation in conformal prediction methods, which traditionally assume ideal conditions and can be undermined by hardware imperfections. AQCP preserves asymptotic average coverage guarantees, ensuring the algorithm’s long-term reliability under arbitrary noise conditions. Experiments conducted on the ibm_sherbrooke quantum processor demonstrate AQCP’s effectiveness. The team implemented AQCP on a univariate multimodal regression task, replicating conditions from prior work to facilitate comparison.

Data collected on April 18th, 2025, from the quantum processor was used to test the algorithm’s local coverage properties. The study also investigated the impact of different score functions and the number of shots on the size of the prediction sets. The researchers evaluated several score functions, including Euclidean Distance, k-Nearest Neighbour (k-NN), Kernel Density Estimation (KDE), and High Density Region (HDR). The model was trained using a hardware efficient ansatz (HEA) with 5 qubits and 5 layers. An angle encoder, a classical neural network with architecture (1, 10, 10, 75), was used to map input features to quantum circuit rotation angles. Visual comparisons of model shots from the Qiskit Aer simulator and the ibm_sherbrooke backend reveal the distribution of predictions, with the component mean functions μ(x) and −μ(x) clearly visible.

Adaptive Conformal Prediction Stabilises Quantum Machine Learning

This work addresses a critical challenge for reliable quantum machine learning: the impact of fluctuating hardware noise on the validity of conformal prediction. The researchers demonstrate that standard conformal prediction methods, which rely on the assumption of stationary noise, can fail when applied to current-generation quantum processors. To overcome this limitation, they introduce Adaptive Conformal Prediction (AQCP), an algorithm designed to maintain accurate coverage guarantees even under arbitrary, time-varying noise conditions. Empirical studies using data from a 16-qubit IBM quantum processor demonstrate that AQCP achieves target coverage levels and exhibits improved stability compared to standard conformal prediction. The theoretical formulation developed alongside the algorithm is expected to benefit practitioners in probabilistic and quantum conformal prediction.