**Learning algorithms for designing efficient, precise, robust, single-shot, quantum-enhanced adaptive parameter estimation policies**

Sequential adaptive measurement is a promising strategy for quantum-enhanced single-shot measurements, but appropriate adaptive procedures are difficult to devise even for ideal cases. Machine-learning techniques enable suitable adaptive policies to be found, but these machine-learning methods are severely limited by computational time and space restrictions. Thus far the collective-intelligence algorithm known as particle swarm optimization has been used to beat the best previous results (obtained by clever guessing) for single-shot adaptive quantum-enhanced measurements of interferometric phase measurement with an entangled multi-photon pulse input state. Specifically, particle swarm optimization previously yielded policies with a space cost that is linear in the number N of operations on the multi-photon pulse and a time that scales as N6 [1-3].
The resultant policy delivers a power-law scaling for the interferometric phase uncertainty phase, ∆φ vs N, but this power law scaling breaks suddenly at N~50 due to a failure of the technique for specific computational resources, namely the number of particles (particle swarm optimization candidate solutions) and number of iterations. Here we devise a far superior algorithm that is able to deliver much better precision for given N with the restriction of using the same computational resources as the competing algorithm. We show that the differential evolution approach to machine learning delivers this same power law scaling as particle swarm optimization and shows no sign of breakdown up to N=100 photons. As the true cost scales as N6, this doubling (at least) of the number of photons actually corresponds to a 64-fold increase in the efficiency of devising the algorithm.