We describe a method for simulating and characterizing realistic Gottesman-Kitaev-Preskill (GKP) cluster states, rooted in the representation of resource states in terms of sums of Gaussian distributions in phase space. We apply our method to study the generation of single-mode GKP states via cat state breeding, and the formation of multimode GKP cluster states via linear optical circuits and homodyne measurements. We characterize resource states by referring to expectation values of their stabilizers and witness operators constructed from them. Our method reproduces the results of standard Fock-basis simulations, while being more efficient and being applicable in a broader parameter space. We also comment on the validity of the heuristic Gaussian random noise model, through comparisons with our exact simulations: We find discrepancies in the stabilizer expectation values when homodyne measurement is involved in cluster state preparation, yet we find close agreement between the two approaches on average.

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• Quantum information architectures & platforms
• Quantum information processing
• Quantum information processing with continuous variables