单向测量模型中几何的一个极值结果
An extremal result for geometries in the one-way measurement model
摘要：
我们提出了一个极端的结果，一类图G（连同一些指定的输入和输出顶点，I和O）有一定的“流”的性质介绍了Danos和Kashefi的单向测量模型的量子计算。三元组（G，I，O）的流的存在允许从单向测量模型中允许的测量基的任何选择导出酉嵌入。我们证明了一个关于图G的边数的上界，使得一个三元组（G，I，O）对某些$I, O \subseteq V(G)$有流，这是根据G和O的顶点数给出的.这意味着当|I| = |O| = k（对应于测量模型中的酉变换）和|V（G）|时间复杂度为O（k^2 n），改进了[quant-ph/0611284]中给出的O（km）的早期已知界限，其中m =| E（G）|.
英文摘要：
We present an extremal result for the class of graphs G which (together with some specified sets of input and output vertices, I and O) have a certain "flow" property introduced by Danos and Kashefi for the one-way measurement model of quantum computation. The existence of a flow for a triple (G,I,O) allows a unitary embedding to be derived from any choice of measurement bases allowed in the one-way measurement model. We prove an upper bound on the number of edges that a graph G may have, in order for a triple (G,I,O) to have a flow for some $I, O \subseteq V(G)$, in terms of the number of vertices in G and O. This implies that finding a flow for a triple (G,I,O) when |I| = |O| = k (corresponding to unitary transformations in the measurement model) and |V(G)| = n can be performed in time O(k^2 n), improving the earlier known bound of O(km) given in [quant-ph/0611284], where m = |E(G)|.
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