Error Correction Codes for Fault-Tolerant Quantum Computation in Superconducting Qubit Architectures
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Fault Tolerance, Surface Code, Superconducting Qubits
Abstract
Fault-tolerant quantum computation remains a central challenge in superconducting qubit architectures, where decoherence, crosstalk, and gate infidelities significantly degrade computational reliability. Although quantum error correction (QEC) codes are widely assumed to provide scalable protection, their practical performance depends critically on hardware-specific noise characteristics that are often underexamined. This study aims to evaluate the effectiveness of leading QEC codes specifically the surface code, Bacon-Shor code, and low-density parity-check (LDPC) quantum codes when implemented on contemporary superconducting qubit platforms. A simulation-based methodological approach is employed, integrating stochastic noise modeling, syndrome extraction analysis, and threshold estimation using density-matrix simulations calibrated with experimentally reported parameters. The results indicate that while the surface code maintains the highest threshold under realistic two-qubit gate fidelities, LDPC-based schemes exhibit superior logical qubit compression but suffer from decoding overhead that limits near-term applicability. The study also identifies parameter regimes where Bacon-Shor codes offer competitive performance due to their reduced measurement complexity. The findings suggest that no single QEC code uniformly outperforms others; instead, code selection must be matched to hardware-specific noise anisotropy and architectural constraints. The research concludes that optimizing QEC for superconducting qubits requires hybrid design strategies that integrate code efficiency with architecture-aware gate scheduling.
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