Adaptive feedback schemes are promising for quantum-enhanced measurements yet are complicated to design. Machine learning can autonomously generate algorithms in a classical setting. Here we adapt machine learning for quantum information and use our framework to generate autonomous adaptive feedback schemes for quantum measurement. 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.
In classical physics, it is assumed that detectors and controls can be arbitrarily accurate, restricted only by technical limitations. However, this paradigm is valid only on a scale where quantum effects can be ignored. The `standard quantum limit’ (SQL) restricts achievable precision, beyond which measurement must be treated on a quantum level. Heisenberg’s uncertainty principle provides a much lower but insurmountable bound for the accuracy of measurement and feedback. Approaching the Heisenberg limit is an important goal of quantum measurement.
Quantum-enhanced measurements are useful for better atomic clocks, gravitational wave detection, and measuring the optical properties of materials.
Particle swarm optimization (PSO) algorithmsremarkably successful for solving non-convex problems. PSO is a `collective intelligence’ strategy from the field of machine learning that learns via trial and error and performs as well as or better than simulated annealing and genetic algorithms. Here we show that PSO algorithms also deliver automated approaches to devising successful quantum measurement policies for implementation in the PU. Our method is effective even if the quantum system is a black box.
In order to show that our method not only works, but is superior to existing feedback-based quantum measurements, we choose the Berry-Wiseman-Breslin (BWB) policy as a benchmark. The BWB-policy is the most precise policy known to date for interferometric phase estimation with direct measurement of the interferometeroutput. Furthermore, its practicality has been demonstrated in a recent experiment
In summary, we have developed a framework which utilizes machine learning to autonomously generate adaptive feedback measurement policies for single parameter estimation problems. Within the limits of the available computational resources, our PSO generated policies achieve an optimal scaling of precision for singleshot interferometric phase estimation with direct measurement of the interferometer output. Our method can be extended to allow training using a real experimental setup by adapting a noise tolerant PSO algorithm. This algorithm does not require prior knowledge about the physical processes involved. Specifically, it can learn to account for all systematic experimental imperfections, thereby making time-consuming error modeling and extensive calibration dispensable.
STRENGTHS OF MACHINE LEARNING SCHEME
* tolerant to photon loss
* estimates ‘ with smallest statistical errors ever achieved
* applicable to any prior distribution of phase ‘
* applicable to any input state j Ni
* technologically feasible
* allows training using a real experiment: algorithm learns to account for systematic experimental imperfections, making error modeling and extensive calibration dispensable