Qubit sensing by optimal narrowband pulses: Demonstration for Rabi frequency sensing

Narrowband optimal control is proposed as a protocol of optimal quantum sensing, providing maximum accuracy for given resources. The procedure is demonstrated on the IBM quantum computer to estimate the amplitude of the qubit Rabi frequency. It is based on optimizing the quantum Fisher information (QFI) when it becomes equal to the classical Fisher information. This scenario offers a practical quantum sensing because it only involves population transfer to the excited state as the target without dynamical phases, which would otherwise be difficult to control and measure. The protocol uses the single-shot-shaped pulse method and an inverse optimization, to design a pulse that results in the optimal QFI in terms of energy or equivalently operating time, referred to in short as local narrowband inverse optimization (NIO). Multiple <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>π</a:mi> </a:math> pulses are shown to be particular cases of this protocol. An alternative semiglobal optimal NIO procedure producing a partially nonoscillatory profile is also demonstrated. Our approach also offers application to optimal atomic selective excitation in an array of atoms for quantum technology.