Quantum-Enhanced Conformal Methods for Multi-Output Uncertainty: A Holistic Exploration and Experimental Analysis

TL;DR

This paper explores the integration of quantum conformal methods with classical distributional prediction to enhance uncertainty quantification in multi-output quantum measurement data, validated through experiments on simulated and real quantum data.

Contribution

It introduces a unified quantum-classical framework combining conformal prediction with quantum measurement data, demonstrating effective coverage guarantees and improved interpretability.

Findings

Classical conformal prediction provides reliable coverage for quantum-derived probabilities.

The approach is validated on both simulated and multi-basis quantum measurement data.

Open-source code and reproducible notebooks are provided for further research.

Abstract

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 multioutput 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.