Exact simulation of photonic continuous-variable cluster states

Properly assessing and optimizing the performance of CV architectures requires an accurate picture of the CV cluster states. A typical approach is to rely on heuristic models like the Gaussian Random Noise (GRN) model, yet this does not capture all the features of the states generated by realistic protocols. We present an approach for exactly simulating of GKP cluster states. We make these computations tractable by using a quasi-analytic phase-space approach, and employing Gaussian expansions for the relevant distributions. We compute logical error rates of four-mode cluster states relevant in the context of quantum repeaters, and we compare our results to earlier estimates based on the GRN model. We highlight discrepancies between our results and those obtained using the GRN model, and the parameter regimes in which these discrepancies are significant. Finally, we discuss prospects for scaling these results to more complex cluster states.