TY - GEN
T1 - Quantum Margulis Codes
AU - Pacenti, Michele
AU - Vasic, Bane
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - Recently, Lin and Pryadko [1] presented the quan-tum two-block group algebra codes, a generalization of bicycle codes obtained from Cayley graphs of non-Abelian groups. We notice that their construction is naturally suitable to obtain a quantum equivalent of the well-known classical Margulis code. In this paper, we first present an alternative description of the two-block group algebra codes using the left-right Cayley complex; then, we show how to modify the construction of Margulis to get a two-block group algebra code. Finally, we construct several quantum Margulis codes and evaluate their performance with numerical simulations.
AB - Recently, Lin and Pryadko [1] presented the quan-tum two-block group algebra codes, a generalization of bicycle codes obtained from Cayley graphs of non-Abelian groups. We notice that their construction is naturally suitable to obtain a quantum equivalent of the well-known classical Margulis code. In this paper, we first present an alternative description of the two-block group algebra codes using the left-right Cayley complex; then, we show how to modify the construction of Margulis to get a two-block group algebra code. Finally, we construct several quantum Margulis codes and evaluate their performance with numerical simulations.
KW - bicycle codes
KW - Margulis code
KW - quantum error correction
KW - Quantum LDPC
KW - two-block group algebra codes
UR - http://www.scopus.com/inward/record.url?scp=85211104999&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85211104999&partnerID=8YFLogxK
U2 - 10.1109/Allerton63246.2024.10735283
DO - 10.1109/Allerton63246.2024.10735283
M3 - Conference contribution
AN - SCOPUS:85211104999
T3 - 2024 60th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2024
BT - 2024 60th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2024
Y2 - 24 September 2024 through 27 September 2024
ER -