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 a 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 provides asymptotic average coverage guarantees under arbitrary hardware noise conditions. Empirical studies on an IBM quantum processor demonstrate that AQCP achieves the target coverage level and exhibits greater stability than quantum conformal prediction.
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 a 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 provides asymptotic average coverage guarantees under arbitrary hardware noise conditions. Empirical studies on an IBM quantum processor demonstrate that AQCP achieves the target coverage level and exhibits greater stability than quantum conformal prediction.
Quantum machine learning is a promising programming paradigm for the optimization of quantum algorithms in the current era of noisy intermediate scale quantum (NISQ) computers. A fundamental challenge in quantum machine learning is generalization, as the designer targets performance under testing conditions, while having access only to limited training data. Existing generalization analyses, while identifying important general trends and scaling laws, cannot be used to assign reliable and informative “error bars” to the decisions made by quantum models. In this article, we propose a general methodology that can reliably quantify the uncertainty of quantum models, irrespective of the amount of training data, of the number of shots, of the ansatz, of the training algorithm, and of the presence of quantum hardware noise. The approach, which builds on probabilistic conformal prediction, turns an arbitrary, possibly small, number of shots from a pre-trained quantum model into a set prediction, e.g., an interval, thatprovablycontains the true target with any desired coverage level. Experimental results confirm the theoretical calibration guarantees of the proposed framework, referred to asquantum conformal prediction.
Quantum fidelity estimation is a fundamental task in quantum information and computing to benchmark the quality of quantum states, and hence of quantum processes, on noisy quantum hardware. Point estimates of fidelity by existing methods generally lack the rigorous uncertainty quantification required for reliable preparation and verification of these tasks. While Bayesian and bootstrap frameworks are widely used for uncertainty quantification, they are sensitive to model misspecification or lack formal coverage guarantees in non-asymptotic regimes. This paper introduces a hybrid "Bayesian-informed" conformal prediction-based framework to provide distribution-free, rigorous prediction intervals for quantum state fidelity estimation which can be used, with care, to approximate confidence intervals with respect to the quantum randomness of Born's rule. The framework requires a point estimator, and we consider both classical point estimators as well as data-driven neural net estimators. We evaluate the robustness of the methodology across a diverse range of experimental challenges, including finite-sample noise, tomographic incompleteness, physical model error, and out-of-distribution data. Our results demonstrate that conformalized estimators maintain statistical validity where traditional methods fail, offering a scalable and reliable approach for the verification of modern quantum systems. The best performing variant of our methodology is based on a class-conditional conformal prediction, as this most closely approximates the conditional coverage desired for a true confidence interval.
Quantum computing introduces unique forms of randomness arising from measurement processes, gate noise, and hardware imperfections. Ensuring reliable uncertainty quantification in such quantum-driven or quantum-derived predictions is an emerging challenge. In classical machine learning, conformal prediction has proven to be a robust framework for distribution-free uncertainty calibration, often focusing on univariate or low-dimensional outputs. Recent advances (e.g., [1–3]) have extended conformal methods to handle multi-output or multi-dimensional responses, addressing sophisticated tasks such as time-series, image classification sets, and quantum-generated probability distributions. However, bridging the gap between these powerful conformal frameworks and the high-dimensional, noise-prone distributions typical of quantum measurement scenarios remains largely open. In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multi-output regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
Quantum machine learning (QML) is a promising paradigm for tackling computational problems that challenge classical AI. Yet, the inherent probabilistic behavior of quantum mechanics, device noise in NISQ hardware, and hybrid quantum-classical execution pipelines introduce new risks that prevent reliable deployment of QML in real-world, safety-critical settings. This research offers a broad roadmap for Trustworthy Quantum Machine Learning (TQML), integrating three foundational pillars of reliability: (i) uncertainty quantification for calibrated and risk-aware decision making, (ii) adversarial robustness against classical and quantum-native threat models, and (iii) privacy preservation in distributed and delegated quantum learning scenarios. We formalize quantum-specific trust metrics grounded in quantum information theory, including a variance-based decomposition of predictive uncertainty, trace-distance-bounded robustness, and differential privacy for hybrid learning channels. To demonstrate feasibility on current NISQ devices, we validate a unified trust assessment pipeline on parameterized quantum classifiers, uncovering correlations between uncertainty and prediction risk, an asymmetry in attack vulnerability between classical and quantum state perturbations, and privacy-utility trade-offs driven by shot noise and quantum channel noise. This roadmap seeks to define trustworthiness as a first-class design objective for quantum AI.
Quantum error correction (QEC) is critical for the reliable implementation of quantum computers, but current QEC protocols often rely on fixed parameters and struggle to adapt to fluctuating environmental noise. This work proposes a novel approach to QEC that leverages machine learning (ML) to dynamically adapt the parameters of QEC protocols in real-time. The core idea involves training neural networks to predict error rates based on observed quantum data and subsequently optimizing the error correction strategies. This adaptive framework offers the potential for significantly improved performance and resilience against evolving noise characteristics. The primary focus is on the theoretical framework and algorithm design, without the need for experimental validation. The proposed method represents a shift from static QEC to a more flexible and efficient system, addressing a key limitation in current quantum computing architectures. The key concept is represented by the following equation: εt = f(xt, θt, η), where εt is the error rate at time *t*, xt is the quantum state at time *t*, θt are the parameters of the QEC protocol at time *t*, and η is the learning rate. This equation highlights the adaptive nature of the system. The efficiency of the system is measured by the reduction in error rates achieved through adaptive parameter adjustment. Further analysis includes the concept of a cost function, C(θ), that represents the overall error correction performance. The goal is to minimize this cost function using the trained neural network. The core of the system relies on a feedback loop – the neural network predicts the error rate, which then influences the adjustment of the QEC protocol parameters.