Quantum Speed Limits in Qubit Dynamics Driven by Bistable Random Telegraph Noise: From Markovian to Non-Markovian Regimes

We investigate the quantum speed limit (QSL) of a single superconducting qubit subjected to pure dephasing induced by bistable random telegraph noise (RTN), a common environmental disturbance in solid state quantum systems. Using an exactly solvable model, we explore how the interplay between RTN parameters the switching rate, coupling strength, and initial condition governs the transition between Markovian and non-Markovian dynamics. A coherence based measure is employed to quantify non-Markovianity, and a unified quantum speed limit bound is derived based on relative purity. Our results reveal that in thermodynamic equilibrium, non-Markovian memory effects significantly reduce the quantum speed limit time, accelerating quantum evolution through information backflow. In contrast, under non-equilibrium initial conditions, the system exhibits purely Markovian behavior regardless of coupling strength, although strong coupling still leads to speedup via enhanced dephasing. These findings offer valuable insights for designing fast and noise resilient quantum protocols by controlling both dynamical parameters and noise initialization.