| Titre | Tradeoffs for reliable quantum information storage in {2D} systems |
| Type de publication | Journal Article |
| Nouvelles publications | 2010 |
| Auteurs | Bravyi S, Poulin D, Terhal BM |
| Journal | Physical Review Letters |
| Volume | 104 |
| Pagination | 050503 |
| Mots clés | Error correction, Self correcting |
| Résumé | We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits $k$, the distance of the code $d$, and the number of particles $n$. It is shown that $kd^2=O(n)$ where the coefficient in $O(n)$ depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. The analogous tradeoff for the classical information storage is $k\sqrt{d} =O(n)$.
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