Beyond average Hamiltonian theory for quantum sensing

The Magnus expansion underpins average Hamiltonian theory (AHT), a central tool in quantum control and sensing that is used to generate efficient approximations of system dynamics. Here, we demonstrate that the conditions for Magnus expansion convergence are violated under typical operating regimes for sensing using solid-state spin systems. We also establish that certain symmetries, such as those found in rapid echo pulse sequences, cancel all higher-order Magnus terms outside standard convergence frameworks. We introduce an exact method to compute the sensor response beyond the AHT regime, and apply it to both broadband and narrow-band magnetometry protocols. Our results clarify AHT limits and enable opportunities in pulse sequence design through symmetry-driven convergence, with implications for entanglement-enhanced sensing and quantum Fisher information estimation in control protocols.