论文标题
在加权图上学习的模棱两可的量子电路
Equivariant quantum circuits for learning on weighted graphs
论文作者
论文摘要
变分量子算法是近期量子硬件优势的领先候选者。当在此设置中训练参数化的量子电路以解决特定问题时，ANSATZ的选择是决定算法的训练性和性能的最重要因素之一。但是，在量子机学习（QML）中，关于训练数据结构激发的Ansatzes的文献很少。在这项工作中，我们介绍了一个ANSATZ，用于在加权图上学习任务，该图形尊重重要的图形对称性，即节点排列下的均衡性。我们评估了该ANSATZ在复杂的学习任务（即神经组合优化）上的表现，在该任务中，机器学习模型用于学习组合优化问题的启发式。我们通过分析和数字研究模型的性能，结果增强了对称性化的Ansatzes是QML成功的关键的观念。
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.
