# Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning

arXiv: https://arxiv.org/abs/2304.03398 · HTML: https://mlsanity.com/paper/2304.03398/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 103 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Plex: Towards Reliability using Pretrained Large Model Extensions](https://mlsanity.com/paper/2207.07411/) (2022)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [An Introduction to Quantum Machine Learning for Engineers](https://mlsanity.com/paper/2205.09510/) (2022)
- [Classification and reconstruction of optical quantum states with deep neural networks](https://mlsanity.com/paper/2012.02185/) (2020)
- [An exponentially-growing family of universal quantum circuits](https://mlsanity.com/paper/2212.00736/) (2022)
- [PACm-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime](https://mlsanity.com/paper/2010.09629/) (2020)
- [Overfitting in quantum machine learning and entangling dropout](https://mlsanity.com/paper/2205.11446/) (2022)
- [Optimizing Partial Area Under the Top-k Curve: Theory and Practice](https://mlsanity.com/paper/2209.01398/) (2022)
- [Discretized conformal prediction for efficient distribution-free inference](https://mlsanity.com/paper/1709.06233/) (2017)
- [Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis](https://mlsanity.com/paper/2209.11514/) (2022)
- [Bayesian Learning of Parameterised Quantum Circuits](https://mlsanity.com/paper/2206.07559/) (2022)
- [Single-preparation unsupervised quantum machine learning: concepts and applications](https://mlsanity.com/paper/2101.01442/) (2021)

## Built on by (most cited first, 11 of 11)

- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Statistical Complexity of Quantum Learning](https://mlsanity.com/paper/2309.11617/) (2023)
- [Cross-Validation Conformal Risk Control](https://mlsanity.com/paper/2401.11974/) (2024)
- [Old Rules in a New Game: Mapping Uncertainty Quantification to Quantum Machine Learning](https://mlsanity.com/paper/2507.14919/) (2025)
- [Uncertainty in Supply Chain Digital Twins: A Quantum-Classical Hybrid Approach](https://mlsanity.com/paper/2411.10254/) (2024)
- [Trustworthy Quantum Machine Learning: A Roadmap for Reliability, Robustness, and Security in the NISQ Era](https://mlsanity.com/paper/2511.02602/) (2025)
- [Quantum Artificial Intelligence for Mission-Critical Systems: Foundations, Architectural Elements, and Future Directions](https://mlsanity.com/paper/2511.09884/) (2025)
- [Detecting underdetermination in parameterized quantum circuits](https://mlsanity.com/paper/2504.03315/) (2025)
- [Assumption-free fidelity bounds for hardware noise characterization](https://mlsanity.com/paper/2504.07010/) (2025)
- [Adaptive Conformal Prediction for Quantum Machine Learning](https://mlsanity.com/paper/2511.18225/) (2025)
- [Conformalized Quantum DeepONet Ensembles: Towards Scalable Operator Learning with Distribution-Free Guarantees](https://mlsanity.com/paper/2605.00330/) (2026)

## Abstract (arXiv)

In this work, we aim at augmenting the decisions output by quantum models with "error bars" that provide finite-sample coverage guarantees. Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. Randomness arises not only from the inherent stochasticity of quantum measurements, but also from quantum gate noise and quantum measurement noise caused by noisy hardware. Furthermore, quantum noise may be correlated across shots and it may present drifts in time. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model. The approach builds on probabilistic conformal prediction (PCP), while accounting for the unique features of quantum models. Among the key technical innovations, we introduce a new general class of non-conformity scores that address the presence of quantum noise, including possible drifts. Experimental results, using both simulators and current quantum computers, confirm the theoretical calibration guarantees of the proposed framework.