Mathematical Formalism of the Gottesman-Kitaev-Preskill code

No Thumbnail Available

Files

URL

Journal Title

Journal ISSN

Volume Title

Perustieteiden korkeakoulu | Bachelor's thesis
Electronic archive copy is available locally at the Harald Herlin Learning Centre. The staff of Aalto University has access to the electronic bachelor's theses by logging into Aaltodoc with their personal Aalto user ID. Read more about the availability of the bachelor's theses.
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.

Authors

Date

2023-09-15

Department

Major/Subject

Quantum Technology

Mcode

SCI3103

Degree programme

Aalto Bachelor’s Programme in Science and Technology

Language

en

Pages

35

Series

Abstract

This thesis explores bosonic quantum error correction, focusing on the GKP (Gottesman-Kitaev-Preskill) code and its mathematical foundations. Beginning with a brief introduction, the thesis covers fundamental quantum mechanics concepts such as qubits and the no-cloning theorem. It then reviews quantum gates, circuits, and error correction techniques, including stabilizer codes and the 5-Qubit Code. The GKP encoding of a single qubit is analyzed of its mathematical constructs and theoretical framework to its last detail. Lattices, Wigner functions, and finite squeezing are examined with their properties proven. GKP codewords are then visualized with the Python package Qutip. This thesis offers a concise yet comprehensive exploration of quantum error correction on a single bosonic qubit, highlighting the potential of the GKP code and its mathematical advantages as a continuous-variable (CV) quantum system. By understanding the mathematical details, we demonstrate the encoding quantum information with the GKP code provides resilience against noise represented by small phase-shift errors.

Description

Supervisor

Raasakka, Matti

Thesis advisor

Kornienko, Vladimir

Keywords

Gottesman-Kitaev-Preskill code, bosonic quantum error correction codes, GKP code

Other note

Citation

Permanent link to this item

https://urn.fi/URN:NBN:fi:aalto-202409176378

Collections

[kand] Perustieteiden korkeakoulu / SCI