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Decoherence limits quantum complexity and thus the quantum advantage that can be achieved on NISQ devices. As a toy model, we study this in a single mode evolving under the nonlinear Kerr interaction. For the closed quantum system, the Kerr interaction is a structure generating process: the Wigner function develops both subPlanckian structure and negativity over time as an initial coherent state evolves into a superposition of many coherent states (the kitten states, which are the higher order generalization of the SchrÃ¶dinger cat state). However, only certain expectation values are sensitive to the coherence and structure of the kitten states, with the expectation values and states connected by the shared symmetry of the finite cyclic group $Z_n$. In the presence of weak decoherence, we find that even these expectation values are increasingly described by the Truncated Wigner Approximation in the largealpha limit, and observe an accompanying general trend of decreased computational cost to numerically predict the measurement outcomes. Lastly, we revisit the question of studying decoherence more broadly, and explore less conventional, stateindependent frameworks for studying decoherence in NISQera devices. Host: Gopikrishnan Muraleedharan 