Mapping graph state orbits under local complementation
Mapping graph state orbits under local complementation
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DOI：
10.22331/q-2020-08-07-305
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发表时间：
2019-10
期刊：
影响因子：
6.4
通讯作者：
J. Adcock;S. Morley-Short;A. Dahlberg;J. Silverstone
中科院分区：
文献类型：
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作者：
J. Adcock;S. Morley-Short;A. Dahlberg;J. Silverstone
图状态及其所具有的纠缠是现代量子计算和通信架构的核心。局部互补——链接所有局部克利福德等效图状态的图操作——允许我们通过纠缠对所有稳定器状态进行分类。在这里，我们研究了局部互补生成的轨道结构，将它们映射到 9 个量子位，并揭示了丰富的隐藏结构。我们提供计算这些轨道的程序，以及 587 个轨道（最多 9 个量子位）中每个轨道的数据以及将其可视化的方法。我们发现某些轨道的连通性与其组成图状态的纠缠性质之间存在直接联系。此外，我们观察了图论轨道特性（例如直径和可着色性）与施密特测量和制备复杂性之间的相关性，并提出了潜在的应用。众所周知，图论和量子纠缠具有很强的相互作用——我们的探索加深了这种关系，为探索纠缠的本质提供了新的工具。
Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation – the graph operation that links all local-Clifford equivalent graph states – allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay – our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.