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Practical effects in the preparation of cluster states using weak non-linearities

We discuss experimental effects in the implementation of a recent scheme for performing bus mediated entangling operations between qubits. Here a bus mode, a strong coherent state, successively undergoes weak Kerr-type non-linear interactions with qubits. A quadrature measurement on the bus then projects the qubits into an entangled state. This approach has the benefit that entangling gates are non-destructive, may be performed non-locally, and there is no need for efficient single photon detection. In this paper we examine practical issues affecting its experimental implementation. In particular, we analyze the effects of post-selection errors, qubit loss, bus loss, mismatched coupling rates and mode-mismatch. We derive error models for these effects and relate them to realistic fault-tolerant thresholds, providing insight into realistic experimental requirements.