Quantum Low-Density Parity-Check Codes
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Perustieteiden korkeakoulu |
Bachelor's thesis
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Date
2024-04-26
Department
Major/Subject
Quantum Technology
Mcode
SCI3103
Degree programme
Aalto Bachelor’s Programme in Science and Technology
Language
en
Pages
27+3
Series
Abstract
Fault-tolerant quantum computing is key in being able to allow businesses and people to start effectively using quantum computing for drug discovery, cryptography, cybersecurity, and many other aspects. In the race to achieve fault-tolerant quantum computing, it is a must to consider the part that quantum error correction plays. Quantum computers will always experience qubit errors, and while this cannot be avoided, quantum error correction provides means to detect and correct errors when they occur. In short, only with the continuous development of better and better quantum error corrections codes will the industry be able to achieve fault-tolerant quantum computing. Surface codes, current quantum error correction codes that are favored in the industry, are highly researched and highly effective. Yet, due to the physical needs for their implementation, there is an incentive in finding quantum error correction codes similar in strength without such overheads. This work explores a potential alternative, low-density parity-check codes, and more specifically, codes in the family of tensor product generalized bicycle codes. Codes in this family have show the capability to rival surface codes made with a large number of physical qubits and large code distances. These rivaling low-density parity-check codes require approximately a seventh of the physical qubits that the equivalent surface codes require. The development of new quantum computers with more and more qubits has been slow. Thus, findings quantum error correction codes that are effective and essentially require less room could prove to become beneficial, efficient, and ultimately, ubiquitous. The above topic is explored in the first part of the thesis through the introduction of quantum error correction, and then the comparison of surface codes to low-density parity-check codes. The second, an applied experiment part of the thesis, explores the creation of a low-density parity-check code in the family of tensor product generalized bicycle codes. Lastly, the conclusion of this thesis summarizes the findings of the comparison between surface codes and low-density parity-check codes along with the results of the experiment.Description
Supervisor
Raasakka, MattiThesis advisor
Raasakka, MattiKeywords
quantum, low-density parity-check, quantum error correction, error correction, surface codes, LDPC