Breuckmann, NP;
Londe, V;
(2022)
Single-Shot Decoding of Linear Rate LDPC Quantum Codes With High Performance.
IEEE Transactions on Information Theory
, 68
(1)
pp. 272-286.
10.1109/TIT.2021.3122352.
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Abstract
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, distance scaling as nϵ for ϵ>0 and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, hyperbolic manifolds, as first suggested by Guth and Lubotzky. The main contribution of this work is the construction of suitable manifolds via finite presentations of Coxeter groups, their linear representations over Galois fields and topological coverings. We establish a lower bound on the encoding rate k/n of 13/72=0.180… and we show that the bound is tight for the examples that we construct. Numerical simulations give evidence that parallelizable decoding schemes of low computational complexity suffice to obtain high performance. These decoding schemes can deal with syndrome noise, so that parity check measurements do not have to be repeated to decode. Our data is consistent with a threshold of around 4% in the phenomenological noise model with syndrome noise in the single-shot regime.
| Type: | Article |
|---|---|
| Title: | Single-Shot Decoding of Linear Rate LDPC Quantum Codes With High Performance |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TIT.2021.3122352 |
| Publisher version: | https://doi.org/10.1109/TIT.2021.3122352 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Technology, Computer Science, Information Systems, Engineering, Electrical & Electronic, Computer Science, Engineering, Quantum codes, quantum error-correction, single-shot decoding, hyperbolic, quantum fault-tolerance, Coxeter groups, cellular automata, belief-propagation, SPACES |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10142042 |
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