Quantum Error Correction

Title

Quantum Error Correction: Decoders for the Toric Code

 Author

Leijenhorst, Nando (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Analysis)

Contributor

Caspers, Martijn (mentor)
Elkouss Coronas, David (mentor)
Ruszel, Wioletta (graduation committee)
Blaauboer, Miriam (graduation committee)

Degree granting institution

Delft University of Technology

 Programme

Applied Mathematics | Applied Physics

 Date

2019-08-30

 Abstract

Quantum error correction is needed for future quantum computers. Classical error correcting codes are not suitable for this due to the nature of quantum mechanics. Therefore, new codes need to be developed. A promising candidate is the toric code, a surface code, because of its locality and its high error correcting capability and thresholds (the error probability below which increasing the size of the code decreases the failure rate). This thesis provides an introduction to quantum error correction and the stabilizer formalism, which is used to introduce the toric code. Several decoders are looked at, including the Minimum Weight Perfect Matching (MWPM) decoder and a recently developed decoder, the Union-Find (UF) decoder. The UF decoder is useful because of its almost-linear time complexity, while only reducing the threshold by a marginal amount compared to the MWPM decoder. In this thesis, the time complexity of the weighted growth version of the UF decoder is analysed. The toric code and the decoders have been implemented and simulated, and the thresholds have been determined. For the MWPM decoder, the threshold was determined to be 11.5±0.2%, which is not in agreement with the threshold in literature of 10.3%, and should not be possible according to the optimal threshold of about 11%. This probably is a result of the low grid sizes (up to a gridsize of 11) of the code used due to the time needed to simulate the MWPM decoder. For the UF decoder, the threshold found was 9.7 ± 0.9%, which is in agreement with the threshold of 9.9% found by N. Delfosse and N. Nickerson. The time complexity of the UF decoder has also been determined, and is indeed almost-linear as expected by the analysis.

 Subject

Quantum Computing
Quantum Error Correction
Quantum Mechanics

 To reference this document use:

http://resolver.tudelft.nl/uuid:94823249-e114-4fc0-bae9-4c80d503296f

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2019 Nando Leijenhorst
Files
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