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arXiv · 1806.06472

Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes

Robert J. Harris·Nathan A. McMahon·Gavin K. Brennen·Thomas M. Stace
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Abstract

We expand the class of holographic quantum error correcting codes by developing the notion of block perfect tensors, a wider class that includes previously defined perfect tensors. The relaxation of this constraint opens up a range of other holographic codes. We demonstrate this by introducing the self-dual CSS heptagon holographic code, based on the 7-qubit Steane code. Finally we show promising thresholds for the erasure channel by applying a straightforward, optimal erasure decoder to the heptagon code and benchmark it against existing holographic codes.

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Robert J. Harris, Nathan A. McMahon, Gavin K. Brennen, Thomas M. Stace. 2018-06-18. Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes. https://doi.org/10.1103/physreva.98.052301

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