Breuckmann, NP;
Eberhardt, JN;
(2021)
Balanced Product Quantum Codes.
IEEE Transactions on Information Theory 2021
, 67
(10)
pp. 6653-6674.
10.1109/TIT.2021.3097347.
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Abstract
This work provides the first explicit and non-random family of [[N,K,D]] LDPC quantum codes which encode K∈Θ(N45) logical qubits with distance D∈Ω(N35) . The family is constructed by amalgamating classical codes and Ramanujan graphs via an operation called balanced product . Recently, Hastings–Haah–O’Donnell and Panteleev–Kalachev were the first to show that there exist families of LDPC quantum codes which break the polylog(N)N−−√ distance barrier. However, their constructions are based on probabilistic arguments which only guarantee the code parameters with high probability whereas our bounds hold unconditionally. Further, balanced products allow for non-abelian twisting of the check matrices, leading to a construction of LDPC quantum codes that can be shown to have K∈Θ(N) and that we conjecture to have linear distance D∈Θ(N) .
| Type: | Article |
|---|---|
| Title: | Balanced Product Quantum Codes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TIT.2021.3097347 |
| Publisher version: | http://dx.doi.org/10.1109/TIT.2021.3097347 |
| 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. |
| 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/10133213 |
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