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Finding flows in the one-way measurement model

Niel de Beaudrap
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Abstract

The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform a unitary embedding between two Hilbert spaces is for the graph G, together with input/output vertices I, O \subset V(G), to have a flow in the sense introduced by Danos and Kashefi [quant-ph/0506062]. For the special case of |I| = |O|, using a graph-theoretic characterization, I show that such flows are unique when they exist. This leads to an efficient algorithm for finding flows, by a reduction to solved problems in graph theory.

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Niel de Beaudrap. 2008-02-29. Finding flows in the one-way measurement model. https://doi.org/10.1103/physreva.77.022328

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