Gate-Based Initialization and Fidelity in Correlated Open Quantum Systems

We present a minimal and general framework for initializing open quantum systems via gate operations, treating system-bath correlations and control dynamics on equal footing. Our protocol simulates thermal equilibration followed by a gate pulse, modeled using a time-dependent Bloch-Redfield equation accurate to second order in coherence. After the gate, the system exhibits hybrid dynamics: populations evolve Markovianly, while coherences dephase as if the system were initially factorized. In fast, strongly dephasing regimes, initial system-bath correlations can revive coherence. Gate fidelities reveal spin-echo-like suppression of errors near 2π rotations, indicating an intrinsic mechanism for error cancellation. The approach is efficient and broadly applicable to both quantum devices and molecular complexes. Applications include fidelity optimization with respect to bath correlation times and coherence tracking in systems such as the Fenna-Matthews-Olson complex. Our results show that long-lived excitonic coherences can arise from strongly non-Markovian dynamics triggered by ultrafast pulses.