Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes

Understand

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.