Feedback ansatz for adaptive-feedback quantum metrology training with machine learning

It is challenging to construct metrology schemes which harness quantum features such as entanglement and coherence to surpass the standard quantum limit. We propose an ansatz for devising an adaptive-feedback quantum metrology (AFQM) strategy which greatly reduces the searching space. Combined with the Markovian feedback assumption, the computational complexity for designing AFQM would be reduced from N-7 to N-4, for N probing systems. The feedback scheme devising via machine learning such as particle-swarm optimization and differential evolution would thus require much less time and produce equally good imprecision scaling. We have thus devised an AFQM for the 207-partite system. The imprecision scaling would persist for N > 207 in an admirable range when the parameter setting for the 207-partite system is employed without further training Our ansatz indicates an built-in resilience of the feedback strategy against qubit loss. The feedback strategies designed for the noiseless scenarios have been tested against the qubit loss noise and the phase fluctuation noise. Our numerical result confirms great resilience of the feedback strategies against the two kinds of noise.