Swarm learning for precise quantum measurements

Quantum measurement schemes aim to surpass the standard quantum limit (essentially due to partition noise) and strive to reach the quantum limit (precision inversely proportional to number of injected particles). Feedback-based schemes are particularly promising: leading particles are detected, and resultant information is fed back to extract progressively more information from subsequent particles. Clever quantum feedback schemes have been devised but are hard to find and are restricted to operating only under ideal conditions. We employ swarm-intelligence learning techniques to obtain autonomous adaptive-feedback quantum measurement schemes. In particular our approach replaces guesswork in quantum measurement by a logical, fully-automatic, programmable routine. We show that our method yields schemes that outperform the best known adaptive scheme for interferometric phase estimation. Furthermore our approach can be adapted to the real-world case where the instrument would learn effective feedback policies through trial and error.