Work

No $((n,K,d< 127))$ Code Can Violate the Quantum Hamming Bound

Year: 2022

Type: article

Abstract: It is well-known that non-degenerate quantum error correcting codes (QECCs) are constrained by a quantum version of the Hamming bound. Whether degenerate codes also obey such a bound, however, remains a long-standing question with practical implications for the efficacy of QECCs. We employ a combination of previously derived bounds on QECCs to demonstrate that a subset of all codes must obey the quantum Hamming bound. Specifically, we combine an analytical bound due to Rains with a numerical bound due to Li and Xing to show that no$((n,K,d))$code with$d< 127$can violate the quantum Hamming bound.

Source: IEEE BITS the Information Theory Magazine

DOI: 10.1109/mbits.2023.3262219

Authors: Emanuel Dallas, Faidon Andreadakis, Daniel Lidar

Institution: University of Southern California

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Army Research Office

Awards: G7452299184, G7833584438