QFI-opt: Identifying optimal quantum states for metrology with noisy hardware

We investigate the use of variational quantum circuits (VQCs) for the preparation of optimal quantum states for metrology in noisy environments using the numerical package QFI-opt. The metrological potential of a given quantum state is quantified by the quantum Fisher information (QFI). Analytic expressions for optimal pure quantum states that maximize the QFI are known. However, an equivalent analytical foundation is lacking for mixed states in open quantum systems and the computation of the QFI is resource intensive. To this end, we carry out a systematic numerical optimization of the QFI for sensing spin rotations using VQCs composed of single qubit rotations and multi-qubit entangling interactions motivated by current capabilities and paradigmatic sensing protocols. We investigate the dependence of the optimal prepared states as a function of decoherence strength and experimentally-motivated noise models. We identify that independent of the nature of the entangling interactions, the optimal prepared states fall into three regimes delineated only by decoherence strength: macroscopic superposition (a.k.a., cat-like) states, squeezed states and unentangled product states. Besides the QFI we compute a range of relevant quantities, including the classical Fisher information, squeezing and counting statistics to classify the states and analyze their suitability for metrology. Our findings are relevant for designing optimal state-preparation strategies for the next-generation of quantum-enhanced sensors aimed at achieving state-of-the-art performance in the presence of noise and decoherence.