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：量子机器学习是当前噪声中等规模量子（NISQ）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础挑战是泛化问题，因为设计者仅在有限训练数据可用的情况下，需针对测试条件下的性能进行优化。现有的泛化分析方法虽能识别重要的总体趋势和标度律，但无法为量子模型决策分配可靠且具有信息量的"误差条"。本文提出一种通用方法论，能够可靠量化量子模型的不确定性，且不受训练数据量、采样次数、拟设、训练算法及量子硬件噪声的影响。该方法基于概率保形预测，可将预训练量子模型的任意少量采样结果转化为集合预测（例如区间），该预测能以任意期望的覆盖水平保证涵盖真实目标。实验结果证实了所提框架（称为量子保形预测）的理论校准保证。