Performance Limits of Fault-Tolerant Quantum Error Correction Schemes

• URL: http://arxiv.org/abs/2605.24501v1
• Date: Sat, 23 May 2026 10:17:42 GMT
• Title: Performance Limits of Fault-Tolerant Quantum Error Correction Schemes
• Abstract summary: We derive bounds for the failure probability of Shor-style FT-QEC schemes using limited structural information.<n>Our analysis separates and quantifies two key contributors to the failure rate: decoding errors and residual errors arising from circuit-level faults.
• Score: 10.119151462781442
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant (FT) implementations. In this paper, we investigate the performance of QEC schemes taking into account that quantum gates and measurements are themselves error-prone. We derive bounds for the failure probability of Shor-style FT-QEC schemes using limited structural information, such as the number of flag qubits and quantum gates. Our analysis separates and quantifies two key contributors to the failure rate: decoding errors and residual errors arising from circuit-level faults. The derived bounds highlight fundamental limitations in Shor-style FT-QEC performance and quantify how circuit imperfections degrade error correction capabilities, under the assumption of depolarizing noise.

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