Variational quantum algorithms are the leading candidate for near-term advantage on noisy quantum hardware. When training a parametrized quantum circuit to solve a specific task, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. Problem-tailored ansatzes have become the standard for tasks in optimization or quantum chemistry, and yield more efficient algorithms with better performance than unstructured approaches. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. Considering that it is widely known that unstructured ansatzes can become untrainable with increasing system size and circuit depth, it is of key importance to also study problem-tailored circuit architectures in a QML context. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task on weighted graphs, where a ML model is used to implement a heuristic for a combinatorial optimization problem. We analytically study the expressivity of our ansatz at depth one, and numerically compare the performance of our model on instances with up to 20 qubits to ansatzes where the equivariance property is gradually broken. We show that our ansatz outperforms all others even in the small-instance regime. Our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML and should be an active area of research in order to enable near-term advantages in this field.

翻译：动态量子算法是紧凑量子硬件近期优势的主要候选条件。 当训练一个可塑性量子电路解决具体任务时, 选择 ansatz 是决定算法的可训练性和性能的最重要因素之一。 问题定制的 ansatze 已经成为优化或量子化学任务的标准, 产生效率更高的算法, 其性能优于非结构化方法。 然而, 在量子机器学习( QML ) 中, 受培训数据结构驱动的关于肛门的文献很少。 考虑到众所周知, 未结构的 ansatze 可能会随着系统大小和电路深度的提高而变得无法操作, 因此, 在 QMML背景下, 也有必要同时研究问题细线电路结构的电路结构结构结构。 在此过程中, 我们引入一个用于在加权图表上学习任务的方法, 也就是在编程中, 等离差不等离差的。 我们评估了这个精细的亚星的性能表现, 在加权的图表中, 将一个我们的数据模型用于在一个智能分析中, 将我们的数据模型用于一个磁性分析的系统, 直径分析。