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Physics Letters A

Quantum control based on machine learning in an open quantum system

Ye‐Xiong Zeng, J. Shen, S. C. Hou, Tesfay Gebremariam Tesfahannes, C. Li

Published Sep 16, 2020• 30 citations
Publisher
DOI
10.1016/j.physleta.2020.126886

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In this work the application of machine learning methods for quantum control of trapped ion quantum computers is studied. This is done in the framework of a single quantum gate, the geometric phase gate. The fundamentals of trapping ions as well as machine learning are presented. The Hamiltoninan operator is derived for a system of two ions in a linear Paul trap. After presenting the consepts of open quantum systems and quantum computing in general, a master equation for two ions in a noisy environment that are driven by a laser is presented. The solution to the master equation is used to generate datasets that corresond to the application of a geometric phase gate. The datasets are then used to train a variety of machine learning models that emulate the mapping from the shape of the control laser all the way to the resulting fidelity of the gate operation. The output of the models is then optimised to acquire the optimal control parameters describing the laser pulse.
The tasks of characterization and control of quantum systems are becoming more challenging with the advancement of quantum technology. Standard methods that were successful for simple quantum systems are becoming inadequate for more complex engineered systems. Modelling assumptions and approximations (such as Markovianity) are not justifiable anymore. As a result, the usual models fail to fit experimental measurements. In this thesis, we use state-of-the-art machine learning methods, assisted by tools from information theory as needed, to develop new frameworks that try to address these challenges. We focus on three directions. The first is developing an efficient online quantum state estimation algorithm with provable convergence properties. The second is developing a deep learning framework for characterizing and controlling closed quantum systems. The final direction is upgrading that framework to be suitable for characterization and control of open quantum systems. This thesis opens the door for a novel way of utilizing machine learning techniques for applications in quantum information specially and physics in general.