Universität zu Köln

Meinerz, Kai ORCID: 0000-0002-9141-7113 (2024). Machine learning assisted Quantum Error Correction and Quantum Feedback Control. PhD thesis, Universität zu Köln.

PDF (Publication of Dissertation) DissertationKaiMeinerz.pdf - Published Version Bereitstellung unter der CC-Lizenz: Creative Commons Attribution Non-commercial. Download (3MB)

Abstract

Quantum feedback control is a field of research that deals with the manipulation of quantum systems towards a goal, based on continuous observation of the systems. These control strategies have been identified as an essential part of the development of future quantum technologies. An example of this is the formulation of quantum error correction strategies for fault-tolerant quantum computing. The design of control strategies is a challenging task, however, as incomplete descriptions of the quantum system at hand and external noise factors often introduce uncertainties into the system, leading to performance degradation. In this thesis, we focus on the use of machine learning based approaches to find quantum control feedback strategies. These approaches have demonstrated the ability to find near-optimal and robust strategies. In a first study, we develop a control strategy for quantum error correction on topological surface codes in the form of a hierarchical decoder. Using a combination of machine learning and combinational decoding, we were able to demonstrate scalable decoding. We achieved nearly linear-time scaling, while still maintaining a high precision decoding comparable to state-of-the-art conventional decoding strategies. The robustness of the decoding strategies is demonstrated through performing tests on different error models including depolarizing noise and faulty syndrome measurements, as well as by changing the underlying error correction code to the rotated surface code. Analyzing the correction applied by the hierarchical decoder provides us with insight into the learned strategies and identifies possible strengths and weaknesses of the decoder, allowing for possible further developments of machine learning and algorithmic decoders based on these findings. In a second study, we investigate the use of reinforcement learning for quantum feedback control. Since reinforcement learning encompasses model-free approaches, it is a prime candidate for finding robust strategies that are not hindered by unknown uncertainties in the experimental system. A well-known problem of reinforcement learning is the sometimes unstable training, caused by the encountered “exploration versus exploitation" dilemma during the process. Therefore, we have implemented a toy model, the quantum cartpole, designed to serve as a benchmark environment for the development of reinforcement learning based quantum feedback strategies. Based on weak measurements, the implemented control strategies have to deal with partial observability and measurement induced feedback. We provide benchmarks for three different variations of the system, including linear and nonlinear systems, using the classical control theory algorithm, linear quadratic Gaussian control, and a reinforcement learning based control strategy. By examining these results, we show the importance of state estimation techniques as part of the control process, and demonstrate the ability of reinforcement to find novel strategies that outperform conventional control strategies in highly nonlinear systems.

Item Type:	Thesis (PhD thesis)
Translated title:	Title Language Maschinelles Lernen unterstützt Quantenfehlerkorrektur und Quantenrückkopplungskontrolle German
Creators:	Creators Email ORCID ORCID Put Code Meinerz, Kai kmeinerz@thp.uni-koeln.de orcid.org/0000-0002-9141-7113 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-734381
Date:	2024
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Unspecified
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language quantum, machine learning, quantum computing, quantum error correction, computational physics, quantum control, quantum feedback control English
Date of oral exam:	15 March 2024
Referee:	Name Academic Title Trebst, Simon Prof. Dr. Gross, David Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/73438