QUANTUM MAXIMUM DISTANCE SEPERABLE CODES

Date

2025-1-10

Author

KIRCALI, MUSTAFA

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Quantum error-correcting codes (QECCs) are a cornerstone of fault-tolerant quantum computing, providing an essential means to protect delicate quantum information from the inevitable errors introduced by decoherence, noise, and operational faults. Unlike classical error correction, which addresses primarily bit-flip errors, QECCs must contend with the more intricate errors that affect both the amplitude and phase of qubits. Among the various types of QECCs, Quantum Maximum Distance Separable (QMDS) codes are particularly noteworthy due to their optimal error correction capabilities, achieving the maximum possible distance for given parameters. Constructing new QMDS codes is a critical challenge in the literature. In this thesis, we study a class of infinitely many explicit polynomials and derive their requisite arithmetical properties, which imply the construction of an infinite family of new q-ary QMDS codes of length strictly larger than q+1. Ball and Vilar demonstrated that the problem of constructing QMDS codes can be reduced to finding specific polynomials over finite fields with well-defined arithmetical properties, yet they were unable to explicitly construct these polynomials.

Subject Keywords

Quantum Error Correction Codes, Hermitian Self-Orthogonal Codes, Reed- Solomon Codes

URI

https://hdl.handle.net/11511/113468

Collections

Graduate School of Applied Mathematics, Thesis