Noise-Resilient Quantum Error Correction Codes Using Superalgebraic Structures

This study explores the development and analysis of quantum error correction codes (QECCs) designed using superalgebraic structures to improve noise resilience in quantum computing systems. The proposed approach integrates the mathematical foundations of Lie superalgebras into the construction of QECCs to enhance their performance under common quantum noise models such as depolarizing, bit-flip, and phase-flip channels. The methodology involves formulating stabilizer generators derived from superalgebraic relations and applying them to simulate quantum channels and perform syndrome extraction. Statistical evaluations and regression-based analyses of fidelity retention and logical error rates are conducted. Results demonstrate a significant reduction in logical error probabilities compared to classical stabilizer codes under identical noise conditions. These findings suggest that superalgebra-informed QECCs can offer a promising path toward scalable, fault-tolerant quantum computing systems. Keywords Quantum error correction, Superalgebraic structures, Lie superalgebras, Noise resilience, Quantum computing, Fidelity analysis