有效可控图
Efficiently Controllable Graphs
摘要：
我们研究的图形，可以断开成小组件，通过删除一个消失的小部分，他们的顶点。我们表明，当一个量子网络描述这样的图，网络是有效的可控的，在这个意义上，通用的量子计算可以使用控制序列多项式的网络的大小，同时控制一个消失的小部分子系统进行。我们表明，对应于有限维晶格的网络是有效可控的，并探索推广到渗流集群和随机图。我们发现，经典的计算复杂性估计的基态的可控图描述的哈密顿量是多项式的子系统/量子比特的数量。
英文摘要：
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that when a quantum network is described by such a graph, the network is efficiently controllable, in the sense that universal quantum computation can be performed using a control sequence polynomial in the size of the network while controlling a vanishingly small fraction of subsystems. We show that networks corresponding to finite-dimensional lattices are efficently controllable, and explore generalizations to percolation clusters and random graphs. We show that the classical computational complexity of estimating the ground state of Hamiltonians described by controllable graphs is polynomial in the number of subsystems/qubits.
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