Cluster state preparation using gates operating at arbitrary success probabilities

Several physical architectures allow for measurement-based quantum computing using sequential preparation of cluster states by means of probabilistic quantum gates. In such an approach, the order in which partial resources are combined to form the final cluster state turns out to be crucially important. We determine the influence of this classical decision process on the expected size of the final cluster. Extending earlier work, we consider different quantum gates operating at various probabilites of success. For finite resources, we employ a computer algebra system to obtain the provably optimal classical control strategy and derive symbolic results for the expected final size of the cluster. We identify two regimes: When the success probability of the elementary gates is high, the influence of the classical control strategy is found to be negligible. In that case, other figures of merit become more relevant. In contrast, for small probabilities of success, the choice of an appropriate strategy is crucial.Comment: 7 pages, 9 figures, contribution to special issue of New J. Phys. on "Measurement-Based Quantum Information Processing". Replaced with published versio

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

The cluster state model for quantum computation has paved the way for schemes that allow scalable quantum computing, even when using non-deterministic quantum gates. Here the initial step is to prepare a large entangled state using non-deterministic gates. A key question in this context is the relative efficiencies of different 'strategies', i.e. in what order should the non-deterministic gates be applied, in order to maximize the size of the resulting cluster states? In this paper we consider this issue in the context of 'large' cluster states. Specifically, we assume an unlimited resource of qubits and ask what the steady state rate at which 'large' clusters are prepared from this resource is, given an entangling gate with particular characteristics. We measure this rate in terms of the number of entangling gate operations that are applied. Our approach works for a variety of different entangling gate types, with arbitrary failure probability. Our results indicate that strategies whereby one preferentially bonds together clusters of identical length are considerably more efficient than those in which one does not. Additionally, compared to earlier analytic results, our numerical study offers substantially improved resource scaling