Optimal Quantum Control with Poor Statistics
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Abstract
Learning how to control a quantum system based on experimental data can help us to exceed the limitations imposed by theoretical modelling. Due to the intrinsic probabilistic nature of quantum mechanics, it is fundamentally necessary to repeat measurements on individual quantum systems many times in order to estimate the expectation value of an observable with good accuracy. Control algorithms requiring accurate data can thus imply an experimental effort that negates the benefits of avoiding theoretical modelling. We present a control algorithm based on Bayesian optimisation that finds optimal control solutions in the presence of large measurement shot noise and even in the limit of single-shot measurements. With the explicit example of the preparation of a GHZ state, we demonstrate in numerical simulations that this method is capable of finding excellent control solutions in terms of minimal experimental effort.