Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem
Diego Ruano, Rodrigo San-Jos\'e
TL;DR
This paper constructs various quantum error-correcting codes using projective Reed-Muller codes, including asymmetric, symmetric, and entanglement-assisted codes, by applying CSS and Hermitian constructions and exploring subfield subcodes.
Contribution
It introduces new quantum codes derived from projective Reed-Muller codes with flexible entanglement and subfield subcodes, expanding the coding options for quantum error correction.
Findings
Constructed asymmetric and symmetric quantum codes from projective Reed-Muller codes.
Developed entanglement-assisted quantum codes with adjustable entanglement.
Created quantum codes from subfield subcodes of projective Reed-Muller codes.
Abstract
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum codes by using the CSS construction and the Hermitian construction, respectively. We provide entanglement-assisted quantum error-correcting codes from projective Reed-Muller codes with flexible amounts of entanglement by considering equivalent codes. Moreover, we also construct quantum codes from subfield subcodes of projective Reed-Muller codes.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata