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.

翻译：本文旨在为量子模型输出决策赋予"误差条"，使其具备有限样本下的覆盖率保证。量子模型通过测量采样实现隐式概率预测器，对每个输入产生多个随机决策。随机性不仅源于量子测量固有的概率特性，还来自噪声硬件导致的量子门噪声和量子测量噪声。此外，量子噪声可能在采样间具有相关性，并随时间呈现漂移现象。本文提出利用此类随机性构建分类与回归任务的预测集，该预测集可被证明能够捕获模型的不确定性。该方法基于概率共形预测框架，同时充分考虑量子模型的独特特性。关键技术突破包括：引入一类新型通用非一致性评分函数，以应对包含潜在漂移在内的量子噪声。基于模拟器和真实量子计算机的实验结果均证实了所提框架的理论校准保证。