TH2.R2.2

Upper bounds on the size of entanglement-assisted codeword stabilized codes using semidefinite programming

Ching-Yi Lai, Pin-Chieh Tseng, National Yang Ming Chiao Tung University, Taiwan; Wei-Hsuan Yu, National Central University, Taiwan
Session:
Quantum Coding Theory 1
Track:
6: Quantum Information and Coding Theory
Location:
Ypsilon I-II-III
Presentation Time:
Thu, 11 Jul, 11:50 - 12:10
Session Chair:
Hiram Lopez,
Abstract
In this paper, we explore the application of semidefinite programming to the realm of quantum codes, specifically focusing on codeword stabilized (CWS) codes with entanglement assistance. Notably, we utilize the isotropic subgroup of the CWS group and the set of word operators of a CWS-type quantum code to derive an upper bound on the minimum distance. Furthermore, this characterization can be incorporated into the associated distance enumerators, enabling us to construct semidefinite constraints that lead to SDP bounds on the minimum distance or size of CWS-type quantum codes. We illustrate several instances where SDP bounds outperform LP bounds.
Session TH2.R2
TH2.R2.1: A Joint Code and Belief Propagation Decoder Design for Quantum LDPC Codes
Sisi Miao, Jonathan Mandelbaum, Holger Jäkel, Laurent Schmalen, Karlsruhe Institute of Technology (KIT), Germany
TH2.R2.2: Upper bounds on the size of entanglement-assisted codeword stabilized codes using semidefinite programming
Ching-Yi Lai, Pin-Chieh Tseng, National Yang Ming Chiao Tung University, Taiwan; Wei-Hsuan Yu, National Central University, Taiwan
TH2.R2.3: Quantum Codes Derived from One-Generator Quasi-Twisted Codes
Akram Saleh, Mohammad Reza Soleymani, Concordia University, Canada
TH2.R2.4: Robust Syndrome Extraction via BCH Encoding
Eren Guttentag, Andrew Nemec, Kenneth R. Brown, Duke University, United States
Resources
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