We provide a mathematically and conceptually robust notion of quantum superpositions of graphs. We argue that, crucially, quantum superpositions of graphs require node names for their correct alignment, which we demonstrate through a no-signalling argument. Nevertheless, node names are a fiducial construct, serving a similar purpose to the labelling of points through a choice of coordinates in continuous space. Graph renamings are understood as a change of coordinates on the graph and correspond to a natively discrete analogue of diffeomorphisms. We postulate renaming invariance as a symmetry principle in discrete topology of similar weight to diffeomorphism invariance in the continuous. We show how to impose renaming invariance at the level of quantum superpositions of graphs.

翻译：我们从数学上和概念上对图形的量子叠加作了一个稳健的概念。我们争论说,关键是,图形的量子叠加需要节点名称才能正确对齐,我们通过无信号参数来证明这一点。然而,节点名称是一个建构,通过在连续空间选择坐标来达到与点标签相似的目的。图重命名被理解为图形上的坐标变化,与本地离散的二异形模拟相对应。我们在离散的地形学中将变异性重新命名为对称原则,其重量与连续变异性相近。我们展示了如何将变异性定在图形量超位水平上。