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. These attacks can undermine both the reliability and security of quantum classification algorithms. In order to develop defence mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in presence of both natural noise sources and adversarial manipulation. From the observation that, unlike in the classical setting, measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing (QHT) and provably robust quantum classification. Then from the optimality of QHT, we prove a robustness condition, which is tight under modest assumptions, and enables us to develop a protocol to certify robustness. Since this robustness condition is a guarantee against the worst-case noise scenarios, our result naturally extends to scenarios in which the noise source is known. Thus we also provide a framework to study the reliability of quantum classification protocols under more general settings.

中文翻译：

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通过量子假设检验优化量子分类的可证明稳健性

与经典模型相比，量子机器学习模型有可能提供加速和更好的预测准确性。然而，这些量子算法，就像它们的经典算法一样，也被证明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现，或者作为最坏的噪声类型，对抗性攻击。这些攻击会破坏量子分类算法的可靠性和安全性。为了开发防御机制并更好地理解这些算法的可靠性，了解它们在存在自然噪声源和对抗性操纵的情况下的鲁棒性特性至关重要。根据观察，与经典环境不同，量子分类算法中涉及的测量自然是概率性的，我们揭示并形式化了二元量子假设检验 (QHT) 和可证明的稳健量子分类之间的基本联系。然后根据 QHT 的最优性，我们证明了稳健性条件，该条件在适度的假设下是严格的，并使我们能够开发一个协议来证明稳健性。由于这种稳健性条件是针对最坏情况噪声场景的保证，因此我们的结果自然会扩展到噪声源已知的场景。因此，我们还提供了一个框架来研究更一般设置下量子分类协议的可靠性。然后根据 QHT 的最优性，我们证明了稳健性条件，该条件在适度的假设下是严格的，并使我们能够开发一个协议来证明稳健性。由于这种稳健性条件是针对最坏情况噪声场景的保证，因此我们的结果自然会扩展到噪声源已知的场景。因此，我们还提供了一个框架来研究更一般设置下量子分类协议的可靠性。然后根据 QHT 的最优性，我们证明了稳健性条件，该条件在适度的假设下是严格的，并使我们能够开发一个协议来证明稳健性。由于这种稳健性条件是针对最坏情况噪声场景的保证，因此我们的结果自然会扩展到噪声源已知的场景。因此，我们还提供了一个框架来研究更一般设置下量子分类协议的可靠性。