Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes
Robert J. Harris, Nathan A. McMahon, Gavin K. Brennen, Thomas M. Stace
TL;DR
This paper introduces a broader class of holographic quantum error correcting codes through block perfect tensors, exemplified by a new 7-qubit Steane code with promising erasure channel thresholds.
Contribution
It develops block perfect tensors, expanding holographic code design, and introduces the self-dual CSS heptagon code based on the Steane code.
Findings
The heptagon code shows promising erasure thresholds.
Block perfect tensors enable a wider class of holographic codes.
Benchmarking indicates competitive performance against existing codes.
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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