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Paper 1
Evolutionary BP+OSD Decoding for Low-Latency Quantum Error Correction
Hee-Youl Kwak, Seong-Joon Park, Hyunwoo Jung, Jeongseok Ha, Jae-Won Kim
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2512.18273
- arXiv
- 2512.18273
We propose an evolutionary belief propagation (EBP) decoder for quantum error correction, which incorporates trainable weights into the BP algorithm and optimizes them via the differential evolution algorithm. This approach enables end-to-end optimization of the EBP combined with ordered statistics decoding (OSD). Experimental results on surface codes and quantum low-density parity-check codes show that EBP+OSD achieves better decoding performance and lower computational complexity than BP+OSD, particularly under strict low latency constraints (within 5 BP iterations).
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Entanglement-assisted Quantum Error Correcting Code Saturating The Classical Singleton Bound
Soham Ghosh, Evagoras Stylianou, Holger Boche
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.04130
- arXiv
- 2410.04130
We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3} $. For higher rates, our EAQECC also meets the Singleton bound, although with increased entanglement requirements. Additionally, we demonstrate that any classical $[n,k,d]_q$ code can be transformed into an EAQECC with parameters $[[n,k,d;2k]]_q$ using $2k$ pre-shared maximally entangled pairs. The complexity of our encoding protocol for $k$-qudits with $q$ levels is $\mathcal{O}(k \log_{\frac{q}{q-1}}(k))$, excluding the complexity of encoding and decoding the classical MDS code. While this complexity remains linear in $k$ for systems of reasonable size, it increases significantly for larger-levelled systems, highlighting the need for further research into complexity reduction.
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