Resource-Aware Quantum Control Under Noise: Deterministic Protocols and Deep Reinforcement Learning

Abstract

We numerically compare quantum-control strategies for few-qubit systems under representative open-system noise and limited control resources. The protocols include shaped pulses, dynamical-decoupling-inspired sequences, hybrid QEC-DD correction, Floquet and Lyapunov control, and deep reinforcement learning (DRL). We benchmark entanglement preservation, entanglement generation, and directed transport under Lindblad decoherence, colored detuning noise, pulse and detuning errors, and imperfect state preparation. The results reveal a resource-dependent hierarchy rather than a universal ranking. A mechanism-resolved pulse analysis shows that sensitivity to colored dephasing is governed by the overlap between the environmental spectrum and the pulse-dependent longitudinal filter function, while absolute performance also depends on pulse-generated coherent dynamics. For six diagnostic pulse families, spectral exposure and the colored-noise-induced change in control-window-averaged concurrence exhibit the same rank ordering. Deterministic pulses remain effective when their temporal and spectral structure matches the task, whereas hybrid QEC-DD benefits from explicit correction resources. In the Floquet setting, DRL can converge to a near-zero-drive boundary when resonant driving is detrimental, closely reproducing no-drive dynamics. Thus, DRL is best viewed as an optimizer over a specified physical control space, whose role depends on the task, reward, observations, and available controls, rather than as a universally superior mechanism.