Tensor-product HDX code[1]
Description
A code constructed in a similar way as the HDX code, but utilizing iterated homological products of multiple Ramanujan complexes and then applying distance balancing. For any fixed tensor-power parameter \(c\), these yield explicit QLDPC codes with distance scaling as \(\sqrt{n}\log^{c} n\), improving on the original HDX construction by replacing a single logarithmic enhancement with arbitrarily high fixed polylogarithmic enhancement. 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 \(\sqrt{n}\log^c n\) for any fixed \(c\), using the \(c\)-fold tensor product of Ramanujan complexes followed by distance balancing [1].Primary Hierarchy
Generalized homological-product qubit CSS codeQLDPC Qubit Generalized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Parents
Tensor-product HDX codes result from iterated homological products of length-two chain complexes (i.e., quantum codes) based on Ramanujan complexes [2].
Tensor-product HDX code
Children
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
- [2]
- N. P. Breuckmann and J. N. Eberhardt, “Quantum Low-Density Parity-Check Codes”, PRX Quantum 2, (2021) arXiv:2103.06309 DOI
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