Emanuele Tirrito

Understanding the complexity of simulating out-of-equilibrium quantum many-body dynamics is a central challenge in quantum physics. In this work, we study this question in the kicked Ising model through two complementary diagnostics: temporal entanglement (TE), which controls the cost of transverse tensor-network contractions, and non-stabilizerness, quantified by the second stabilizer Rényi entropy. Focusing on the transverse boundary vectors generated in transverse light-cone contraction, we analyze how these quantities scale in proximity to classical limits, the dual-unitary point, and inside the generic non-integrable regimes. Although spatial and temporal entanglement are expected to scale linearly in generic non-integrable and dual unitary settings, our results present a multifaceted perspective. TE scaling is substantially more nuanced than the generic volume-law expectation. Although it vanishes at the classical points, it behaves quite differently around them, demonstrating sub-linear growth or area-law saturation depending on the classical point. It also vanishes at the dual-unitary point, but is restored to volume-law growth by infinitesimal detuning. By contrast, non-stabilizerness shows a much simpler pattern, growing linearly through most of the parameter space, with its main qualitative exception again at dual unitarity, where it also vanishes. Our results have implications for the potential efficiency of transverse folding methods in the kicked Ising model, while also underscoring that complexity is multifaceted and cannot be inferred from one notion alone.