Optimal Single-Shot Decoding of Quantum Codes

• URL: http://arxiv.org/abs/2310.18138v2
• Date: Tue, 19 Mar 2024 15:53:56 GMT
• Title: Optimal Single-Shot Decoding of Quantum Codes
• Authors: Aldo Cumitini, Stefano Tinelli, Balázs Matuz, Francisco Lázaro, Luca Barletta,
• Abstract summary: We discuss single-shot decoding of quantum Calderbank-Shor-Steane codes with faulty syndrome measurements. By adding redundant rows to the code's parity-check matrix we obtain an additional syndrome error correcting code.
• Score: 4.233908672338595
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss single-shot decoding of quantum Calderbank-Shor-Steane codes with faulty syndrome measurements. We state the problem as a joint source-channel coding problem. By adding redundant rows to the code's parity-check matrix we obtain an additional syndrome error correcting code which addresses faulty syndrome measurements. Thereby, the redundant rows are chosen to obtain good syndrome error correcting capabilities while keeping the stabilizer weights low. Optimal joint decoding rules are derived which, though too complex for general codes, can be evaluated for short quantum codes.

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