Noise structuring in fixed-depth Trotter simulation: stationary channels and observable-level depolarization
We analyze fixed-depth Trotter simulation as a method for structuring hardware noise in digital many-body dynamics. The number of layers is chosen using the largest endpoint time and is then kept fixed throughout the time scan, making the total noise dose approximately independent of the endpoint time. For local stochastic faults, we show that, once propagated faults lose memory of their insertion layer, the noisy circuit factorizes into ideal evolution followed by a stationary finite-depth binomial channel. In the dilute-layer limit, this channel reduces to a Poissonian exponential. The memory time of a single fault is related to a Loschmidt echo. An important consequence is observable-level depolarization: for selected macroscopic observables at low to moderate noise levels, the stationary channel can act as an almost time-independent affine contrast correction, even though the full channel need not be depolarizing, which is crusial for error mitigation purposes. At short times, the same protocol produces a digital Zeno-like transient, in which a fixed number of noise opportunities competes with a vanishing coherent angle per layer. Our results also reveal limitations of naive zero-noise extrapolatin strategies based on oversimplified functions.