Quantum Error-Correction for Distributed Quantum Computing: Decoding Performance of Entanglement-Assisted Stabilizer Codes with Noisy Ebits
Translated title
Quantum Error-Correction for Distributed Quantum Computing
Author
Søndergaard, Jakob Kaltoft
Term
4. semester
Education
Publication year
2024
Submitted on
2024-06-03
Pages
134
Abstract
Quantum computers promise significant advances, but their high error rates remain a major obstacle. This thesis investigates how quantum error-correcting codes can mitigate errors in a distributed setting, focusing on entanglement-assisted (EA) stabilizer codes that assume pre-shared entanglement between sender and receiver. Because the common assumption that the receiver’s half of the shared ebits is noiseless is difficult to meet in practice, the thesis examines the impact of allowing noise on the receiver’s ebits. A method is developed to analyze depolarizing noise for the [[6, 1, 3; 1]] EA code, identifying which error patterns are correctable and assessing decoding performance based on the likelihood of such errors. The same approach is applied to the [[5, 1, 3; 2]] EA code, enabling a comparison between the two. The results show that both codes can still correct certain errors with noisy ebits, but performance degrades markedly as noise on the receiver’s half increases; moreover, [[5, 1, 3; 2]] generally outperforms [[6, 1, 3; 1]] under the studied conditions. These findings highlight the importance of modeling and addressing noise on the receiver’s ebits in distributed quantum computing.
Kvantecomputere lover store fremskridt, men deres høje fejlrate er en stor hindring. Dette speciale undersøger, hvordan kvantefejl kan afhjælpes i en distribueret sammenhæng ved hjælp af kvantefejlrettende koder, med fokus på sammenfiltningsstøttede (entanglement‑assisted, EA) stabiliseringskoder, som forudsætter foruddelt sammenfiltring mellem afsender og modtager. I praksis er antagelsen om, at modtagerens halvdel af de delte ebits er fejlfri, svær at opfylde; specialet analyserer derfor konsekvenserne af at tillade støj på modtagerens ebits. Der udvikles en metode til at analysere depolariserende støj for [[6, 1, 3; 1]]‑EA‑koden, der identificerer hvilke fejlmønstre der kan rettes, og vurderer afkodningsydeevnen ud fra sandsynligheden for, at sådanne fejl opstår. Den samme tilgang anvendes på [[5, 1, 3; 2]]‑EA‑koden, og de to koder sammenlignes. Resultaterne viser, at begge koder kan rette visse fejl selv med støjende ebits, men at ydeevnen reduceres markant, når støjen på modtagerens halvdel øges; desuden har [[5, 1, 3; 2]]‑koden generelt bedre ydeevne end [[6, 1, 3; 1]] under de undersøgte forhold. Arbejdet understreger vigtigheden af at modellere og håndtere støj på modtagerens ebits i distribueret kvanteberegning.
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