The introduction of the European Union's (EU) set of comprehensive regulations relating to technology, the General Data Protection Regulation, grants EU citizens the right to explanations for automated decisions that have significant effects on their life. This poses a substantial challenge, as many of today's state-of-the-art algorithms are generally unexplainable black boxes. Simultaneously, we have seen an emergence of the fields of quantum computation and quantum AI. Due to the fickle nature of quantum information, the problem of explainability is amplified, as measuring a quantum system destroys the information. As a result, there is a need for post-hoc explanations for quantum AI algorithms. In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post-hoc explanations. However, this approach does not translate to use in quantum computing trivially and can be exponentially difficult to implement if not handled with care. We propose a novel algorithm which reduces the problem of accurately estimating the Shapley values of a quantum algorithm into a far simpler problem of estimating the true average of a binomial distribution in polynomial time.

翻译：欧盟（EU）发布的一系列全面的技术相关法规，《通用数据保护条例》，赋予了欧盟公民对其生活中产生重大影响的自动化决策获得解释的权利。这带来了重大挑战，因为当今许多最先进的算法通常都是无法解释的黑箱。与此同时，我们目睹了量子计算和量子人工智能领域的兴起。由于量子信息的不稳定性，可解释性问题被进一步放大——测量量子系统会破坏信息。因此，需要为量子人工智能算法提供事后解释。在经典背景下，合作博弈论中的夏普利值概念已被用于事后解释。然而，这种方法无法简单地迁移至量子计算领域，若不谨慎处理，其实现复杂度可能呈指数级增长。我们提出了一种新颖的算法，该算法将准确估计量子算法夏普利值的问题简化为一个更简单的问题：在多项式时间内估计二项分布的真实均值。