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Title Implementing quantum error correcting codes with quantum neural networks
Author Θεοχαράκης, Μύρων
Thesis advisor Τσιρώνης, Γεώργιος
Μπαρμπαρής, Γεώργιος
Abstract The main purpose of this thesis is to examine and evaluate quantum error-correcting methods arising from the use of quantum neural networks. More specifically we focus on error-correcting arbitrary qubit states, that are exposed to certain kinds of quantum noise, with the use of Quantum Autoencoders. The task of our models is to discover quantum operations that can identify and correct the effects of quantum noise in a corrupted qubit state. After an intensive introduction to quantum error correction and to the structure of Quantum Autoencoders, we present the results produced by models deployed for error-correcting the Bit Fip channel and the Amplitude Damping channel that take advantage of preexisting codewords for creating logical qubits. Both of these quantum channels can be successfully corrected via other methods of performing quantum error correction. Our aim is to provide a proof of concept for further investigation of the abilities of these kinds of Neural Networks. The results of error-correcting qubit states affected by the Bit Flip channel are satisfying. The average Fidelity between the output of the model and the original uncorrupted state is F¯ = 0.90. However, training these models is an extremely hard task as they are extremely sensitive to overfitting or reaching a local maximum of their cost function. The initial results from training QAEs for error-correcting the Amplitude Damping were not so encouraging. To error-correct this quantum channel we had to create a new structure of layers that we named Conjugate Layers. By implementing QAEs that contained Conjugate Layers we manage to produce some satisfying results (F¯ = 0.87). However, we must highlight the fact that we dealt with the simplest form of Amplitude Damping with the probability of spontaneous decay being γ = 0.1. Because of the simplicity of our task we expected higher values of the average Fidelity to feel more confident to deal with a more complex case.
Language English
Issue date 2022-11-25
Collection   School/Department--School of Sciences and Engineering--Department of Physics--Graduate theses
  Type of Work--Graduate theses
Permanent Link https://elocus.lib.uoc.gr//dlib/2/f/3/metadata-dlib-1666873147-260290-28863.tkl Bookmark and Share
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