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, that provably contains the true target with any desired coverage level. Experimental results confirm the theoretical calibration guarantees of the proposed framework, referred to as quantum conformal prediction.

翻译：量子机器学习是在当前含噪中等规模量子计算机时代优化量子算法的一种有前景的编程范式。量子机器学习中的一个基本挑战是泛化问题：设计者仅能访问有限的训练数据，却需要针对测试条件下的性能进行优化。现有泛化分析虽然揭示了重要的总体趋势和标度律，但无法为量子模型的决策分配可靠且有信息量的“误差棒”。本文提出一种通用方法论，无论训练数据量、测量次数、拟设、训练算法及量子硬件噪声存在与否，均可可靠地量化量子模型的不确定性。该方法基于概率共形预测，将预训练量子模型中任意（可能极少量）的测量结果转化为集合预测（例如区间），并能以任意期望的覆盖水平保证该预测包含真实目标。实验结果证实了所提出框架（称为量子共形预测）的理论校准保证。