Tensor-product HDX code[1]
Description
Code constructed in a similar way as the HDX code, but utilizing tensor products of multiple Ramanujan complexes and then applying distance balancing. These improve the asymptotic code distance over the HDX codes 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
- Generalized homological-product qubit CSS code — Tensor-product HDX codes result from a iterated tensor products of Ramanujan complexes.
Child
- High-dimensional expander (HDX) code — Ramanujan codes result from a tensor product of a classical-code and a quantum-code chain complex.
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
Page edit log
- Victor V. Albert (2022-10-02) — most recent
Cite as:
“Tensor-product HDX code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/iterated_ramanujan