Compare Papers
Paper 1
A simple decoder for topological codes
James R. Wootton
- Year
- 2013
- Journal
- arXiv preprint
- DOI
- arXiv:1310.2393
- arXiv
- 1310.2393
Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both i.i.d. and spatially correlated errors and is found to compare well with existing methods.
Open paperPaper 2
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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