Performance Analysis of Topological Quantum Error Correcting Codes

Forlivesi, Diego (2022) Performance Analysis of Topological Quantum Error Correcting Codes. [Laurea magistrale], Università di Bologna, Corso di Studio in Ingegneria elettronica e telecomunicazioni per l'energia [LM-DM270] - Cesena, Documento full-text non disponibile
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In the last few years there has been a great development of techniques like quantum computers and quantum communication systems, due to their huge potentialities and the growing number of applications. However, physical qubits experience a lot of nonidealities, like measurement errors and decoherence, that generate failures in the quantum computation. This work shows how it is possible to exploit concepts from classical information in order to realize quantum error-correcting codes, adding some redundancy qubits. In particular, the threshold theorem states that it is possible to lower the percentage of failures in the decoding at will, if the physical error rate is below a given accuracy threshold. The focus will be on codes belonging to the family of the topological codes, like toric, planar and XZZX surface codes. Firstly, they will be compared from a theoretical point of view, in order to show their advantages and disadvantages. The algorithms behind the minimum perfect matching decoder, the most popular for such codes, will be presented. The last section will be dedicated to the analysis of the performances of these topological codes with different error channel models, showing interesting results. In particular, while the error correction capability of surface codes decreases in presence of biased errors, XZZX codes own some intrinsic symmetries that allow them to improve their performances if one kind of error occurs more frequently than the others.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Forlivesi, Diego
Relatore della tesi
Correlatore della tesi
Corso di studio
Ordinamento Cds
Parole chiave
Quantum Error Correcting Codes,Surface Codes,XZZX Codes,Minimum Weight Perfect Matching,Quantum Internet
Data di discussione della Tesi
30 Settembre 2022

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