Our preliminary investigations indicate that U(1) symmetrical random circuits generate states with maximal (conditional) Neumann entropy. In particular, in the Jz= 0 sector we expect to generate an ensemble of entangled Dicke-like states, useful for quantum metrology. We shall explore how the metrological usefulness depends in this case on the initial state, the circuit depth, and Jz. We shall also produce metrologically useful U(1) symmetrical states on the IBM and QuEra platforms and study their structure and sensitivity. We shall explore robustness against dissipation, relevant for all experimental realizations.

This research shall be financed completely or in part by the Advanced NKFIH grant "Design and application of advanced techniques for quantum metrology, simulation, and optimization".