Tensor-product HDX code[1] 

Description

Code constructed in a similar way as the HDX code, but utilizing tensor products of Ramanujan complexes in order to improve code distance from \(\sqrt{n}\log n\) to \(\sqrt{n}~\text{polylog}(n)\). The utility of such tensor products comes from the fact that one of the Ramanujan complexes is a collective cosystolic expander as opposed to just a cosystolic expander.

Protection

Construction yields explicit QLDPC codes with distance \(\sqrt{n}\log^c n\) using the \(c\)-tensor-product of Ramanujan complexes.

Parent

References

[1]
T. Kaufman and R. J. Tessler, “New Cosystolic Expanders from Tensors Imply Explicit Quantum LDPC Codes with \(Ω(\sqrt{n}\log^kn)\) Distance”, (2020) arXiv:2008.09495
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Zoo Code ID: iterated_ramanujan

Cite as:
“Tensor-product HDX code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/iterated_ramanujan
BibTeX:
@incollection{eczoo_iterated_ramanujan, title={Tensor-product HDX code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/iterated_ramanujan} }
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Permanent link:
https://errorcorrectionzoo.org/c/iterated_ramanujan

Cite as:

“Tensor-product HDX code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/iterated_ramanujan

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/qldpc/homological/iterated_ramanujan.yml.