Finding flows in the one-way measurement model

Details Finding flows in the one-way measurement model Finding flows in the one-way measurement model

2006-11-29

arxiv.org/abs/quant-ph/0611284v3

Phys. Rev. A 77, 022328 (2008)

Physics

Quantum Physics

8 pages, 3 figures: somewhat condensed and updated version, to appear in PRA

Scientific paper

10.1103/PhysRevA.77.022328

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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