Quantum Lunch: General Error Correction for MERA Codes

Speaker: Francesco Battistel

Title:
General Error Correction for MERA Codes

Abstract:
The Multi-Scale Entanglement Renormalization Ansatz (MERA), introduced by Vidal in 2005, is a tensor network which has proven to be useful to represent many-body states where entanglement is gradually introduced at different scales, in a local way at each scale. In particular, a MERA can be viewed as the encoding circuit for a family of quantum error correcting codes.

Our motivation for studying such codes comes, on the one hand, from the fact that there are good codes which have a MERA representation, like the toric code, and, on the other hand, from a recent work by Kim & Kastoryano (arXiv:1701.00050), in which the authors exploit the causal structure of entanglement renormalization to derive bounds on the ability of MERA codes to correct erasure errors.

We ask if it is possible to construct other good codes with the structure of a MERA and if entanglement renormalization can give useful information for a decoding procedure. Moreover, using a notion of approximate error correction given by Bény & Oreshkov, we explore the possibility of generalizing the bounds derived by Kim & Kastoryano to arbitrary errors. This is a work done as part of my Master thesis project under the supervision of Prof. Robert König at TU Munich.