Quantum metrology with full and fast quantum control

We establish general limits on how precise a parameter, e.g., frequency or the strength of a magnetic field, can be estimated with the aid of,call and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that fast control allows to fully restore the Heisenberg scaling (similar to 1/N-2) for all rank-one Pauli noise except dephasing. For all other types of noise the asymptotic quantum enhancement is unavoidably limited to a constant-factor improvement over the standard quantum limit (similar to 1/N) even when allowing for the full power of fast control. The hitter holds both in the single-shot and infinitely many repetitions scenarios. However, even in this case allowing for fast quantum control helps to improve the asymptotic constant factor. Furthermore, for frequency estimation with finite resource we show how a parallel scheme utilizing any fixed number of entangled qubits hut no fast quantum control can he outperformed by a simple, easily implementable, sequential scheme which only requires entanglement between one sensing and one auxiliary qubit.