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Recent quantum simulation by Google [Nature 612, 240 (2022)] has demonstratedthe formation of bound states of interacting photons in a quantum-circuitversion of the XXZ spin chain. While such bound states are protected byintegrability in a one-dimensional chain, the experiment found the bound statesto be unexpectedly robust when integrability was broken by decorating thecircuit with additional qubits, at least for small numbers of qubits ($\leq24$) within the experimental capability. Here we scrutinize this result bystate-of-the-art classical simulations, which greatly exceed the experimentalsystem sizes and provide a benchmark for future studies in larger circuits. Wefind that the bound states consisting of a small and finite number of photonsare indeed robust in the non-integrable regime, even after scaling to theinfinite time and infinite system size limit. Moreover, we show that suchsystems possess unusual spectral properties, with level statistics thatdeviates from the random matrix theory expectation. On the other hand, for lowbut finite density of photons, we find a much faster onset of thermalizationand significantly weaker signatures of bound states, suggesting that anomalousdynamics may only be a property of dilute systems with zero density of photonsin the thermodynamic limit. The robustness of the bound states is alsoinfluenced by the number of decoration qubits and, to a lesser degree, by theregularity of their spatial arrangement.

Integrability breaking and bound states in Google's decorated XXZ circuits