Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.

与传统的机器模型相比，量子机器学习模型具有提速和更好的预测准确性的潜力。然而，这些量子算法，像它们的经典算法一样，也被证明也容易受到输入扰动的影响，特别是对于分类问题。这些可能来自嘈杂的实施，也可能来自对抗性攻击（在最坏的情况下为噪声）。为了开发防御机制并更好地理解这些算法的可靠性，在存在自然噪声源或对抗性操纵的情况下，了解它们的鲁棒性至关重要。从观察到，量子分类算法中涉及的测量是自然概率的，我们发现并形式化了二进制量子假设测试与可证明的鲁棒量子分类之间的基本联系。此链接导致严格的鲁棒性条件，该条件对分类器可容忍的噪声量施加了约束，而与噪声源是自然噪声还是对抗噪声源无关。基于此结果，我们开发了实用的协议以最佳地证明鲁棒性。最后，由于这是针对最坏情况下的噪声的鲁棒性条件，因此我们的结果自然会扩展到已知噪声源的场景。因此，我们还提供了一个框架来研究量子模型分类协议在对抗性，最坏情况下的噪声情况以外的可靠性。与噪声源是自然噪声还是对抗噪声无关。基于此结果，我们开发了实用的协议以最佳地证明鲁棒性。最后，由于这是针对最坏情况下的噪声的鲁棒性条件，因此我们的结果自然会扩展到已知噪声源的场景。因此，我们还提供了一个框架来研究量子模型分类协议在对抗性，最坏情况下的噪声情况以外的可靠性。与噪声源是自然噪声还是对抗噪声无关。基于此结果，我们开发了实用的协议以最佳地证明鲁棒性。最后，由于这是针对最坏情况下的噪声的鲁棒性条件，因此我们的结果自然会扩展到已知噪声源的场景。因此，我们还提供了一个框架来研究量子模型分类协议在对抗性，最坏情况下的噪声情况以外的可靠性。