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The cluster state model for quantum computation has paved the way for schemesthat allow scalable quantum computing, even when using non-deterministicquantum gates. Here the initial step is to prepare a large entangled stateusing non-deterministic gates. A key question in this context is the relativeefficiencies of different `strategies', i.e. in what order should thenon-deterministic gates be applied, in order to maximize the size of theresulting cluster states? In this paper we consider this issue in the contextof `large' cluster states. Specifically, we assume an unlimited resource ofqubits and ask what the steady state rate at which `large' clusters areprepared from this resource is, given an entangling gate with particularcharacteristics. We measure this rate in terms of the number of entangling gateoperations that are applied. Our approach works for a variety of differententangling gate types, with arbitrary failure probability. Our results indicatethat strategies whereby one preferentially bonds together identical qubits areconsiderably more efficient than those in which one does not. Additionally,compared to earlier analytic results, our numerical study offers substantiallyimproved resource scaling.Comment: 9 pages, 7 figure

Strategies for the preparation of large cluster states using non-deterministic gates