Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. 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, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.

翻译：变分量子算法是近期量子硬件上实现优势的主要候选方案。在此框架下训练参数化量子电路以解决特定问题时，拟设的选择是决定算法可训练性与性能的最关键因素之一。然而，在量子机器学习领域，基于训练数据结构设计的拟设研究仍较为匮乏。本文针对加权图学习任务，提出了一种尊重重要图对称性（即节点排列等变性）的拟设。我们在复杂学习任务——神经组合优化（利用机器学习模型学习组合优化问题启发式策略）中评估了该拟设的性能。通过解析与数值方法研究模型表现，我们的研究结果进一步证实了保对称性拟设在量子机器学习成功中的关键作用。