
TL;DR
This paper introduces a geometric framework for constructing quantum error-correcting codes using orbifold and weighted projective structures, leading to new bounds and explicit code examples.
Contribution
It develops a novel geometric approach linking orbifold theory with quantum code construction, including a refined Singleton bound and practical code examples.
Findings
Construction of Quantum Weighted Algebraic Geometric (QWAG) codes.
A refined Singleton-type bound incorporating orbifold geometry.
Explicit code examples and computational tools in Sage/Python.
Abstract
This work develops a geometric framework for constructing quantum error-correcting codes from weighted projective and orbifold structures, integrating algebraic geometry, divisor theory, and the CSS stabilizer formalism. Beginning with weighted projective spaces and their associated height and defect structures, the study builds classical AG-codes via evaluation on divisors adapted to orbifold singularities. These classical codes are lifted to quantum codes using self-orthogonality conditions and homological constructions, yielding a class of Quantum Weighted Algebraic Geometric (QWAG) codes. A central contribution is the formulation of a refined Singleton-type bound motivated by orbifold defect terms and effective genus corrections. While the classical quantum Singleton bound is recovered in the smooth case, the orbifold setting suggests additional geometric contributions that may…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Algebraic structures and combinatorial models · Quantum Information and Cryptography
