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arXiv · 1312.4578

Tensor Networks and Quantum Error Correction

Andrew J. Ferris·David Poulin
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Abstract

We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.

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Andrew J. Ferris, David Poulin. 2014-06-25. Tensor Networks and Quantum Error Correction. https://doi.org/10.1103/physrevlett.113.030501

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