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Holographic Code Rate
August 25, 2019 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Noah Bray-Ali, David Chester, Dugan Hammock, Marcelo M. Amaral, Klee Irwin, Michael F. Rios
arXiv ID
1908.09253
Category
quant-ph: Quantum Computing
Cross-listed
cs.IT,
hep-th
Citations
1
Venue
arXiv.org
Last Checked
5 months ago
Abstract
Holographic codes grown with perfect tensors on regular hyperbolic tessellations using an inflation rule protect quantum information stored in the bulk from errors on the boundary provided the code rate is less than one. Hyperbolic geometry bounds the holographic code rate and guarantees quantum error correction for codes grown with any inflation rule on all regular hyperbolic tessellations in a class whose size grows exponentially with the rank of the perfect tensors for rank five and higher. For the tile completion inflation rule, holographic triangle codes have code rate more than one but all others perform quantum error correction.
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