Abstract
Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many scenarios, the prerequisite condition of faithfully preparing a desired quantum state despite decoherence and system imperfections is not always adequately met. To pave the way to a specific target state, we implement quantum optimal control based on Bayesian optimization. The probabilistic modeling and broad exploration aspects of Bayesian optimization are particularly suitable for quantum experiments where data acquisition can be expensive. Using numerical simulations for the superfluid to Mott-insulator transition for bosons in a lattice as well as for the formation of Rydberg crystals as explicit examples, we demonstrate that Bayesian optimization is capable of finding better control solutions with regards to finite and noisy data compared to existing methods of optimal control.
Highlights
In this paper, the focus is on creating spatially ordered states in two different ultra-cold systems, atoms in optical lattice and highly excited Rydberg atoms, as testbeds for Bayesian optimization
Using numerical simulations for the superfluid to Mott-insulator transition for bosons in a lattice as well as for the formation of Rydberg crystals as explicit examples, we demonstrate that Bayesian optimization is capable of finding better control solutions with regards to finite and noisy data compared to existing methods of optimal control
The essential steps of Bayesian optimization (BO) used for quantum optimal control are shown in figure 1 and are discussed : BO relies on an approximate model of the optimization landscape, which is updated at each iteration, and is leveraged to choose the set of parameters for which the figure of merit (FoM) is evaluated
Summary
Rick Mukherjee1 , Frédéric Sauvage1, Harry Xie1, Robert Löw2 and Florian Mintert1 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Keywords: machine learning, Bayesian optimisation, Bose–Hubbard model, superfluid to Mott insulator transition, Rydberg atoms, ultra-cold gases, atoms in optical lattice
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