Characterizing phase fragility via algorithmically prepared ancillas in repeated-interaction models

We study how a phase parameter (Formula presented) (Formula presented), encoded through a single-qubit (Formula presented) (Formula presented) gate sequence, is reflected in the quantum fisher information (QFI) under realistic noisy dynamics. Within a collision-model framework, a probe qubit interacts sequentially with algorithmically prepared reservoir ancillas, leading to a (Formula presented) (Formula presented) -dependent steady state from which (Formula presented) (Formula presented) can be evaluated in closed form. In parallel, we perform pulse-resolved open-system simulations of the same gate sequence, using Gaussian-driven control motivated by transmon hardware, to obtain the corresponding pre-measurement density matrix. Despite the distinct physical descriptions, both approaches yield QFI profiles with similar phase dependence on the encoded phase. A quantitative comparison using profile-level similarity metrics further shows that the two descriptions identify the same phase-sensitive regions, although their absolute QFI contrasts differ. This consistency indicates that the steady state of a probe qubit interacting with algorithmically prepared ancillas can capture key features of the phase response observed in noisy device-level implementations. The underlying physical mechanism is the persistence of finite steady coherence in the asymptotic probe state, which retains the phase imprint of the prepared ancillas. Beyond conceptual insight, the steady-state framework provides a model-based, tomography-free diagnostic route for characterizing phase sensitivity. Possible uses in biased-noise error correction, hardware-aware compilation, and pulse-level optimization are therefore presented as future outlook directions.