Quantum Error-Correction Properties of Hyperinvariant Tensor Networks

Hyperinvariant tensor networks were developed in order to provide simulations of Conformal Field-Theoretic states in the context of the AdS/CFT correspondence. We show that the original construction is generalizable using the quantum Fourier transform and k-Uniform maximally-entangled quantum states. Additionally, we show that a hyperinvariant tensor network can be modified as a quantum error-correction code, and that the rate of many example code families are finite. Finally, we report on the practical applicability of these new quantum error-correction code families by performing analytical and numerical threshold studies. Our work is anticipated to stimulate a larger conversation on holographic quantum error correction, as well as simulations of conformal field theory in the context of hyperbolic tensor-network constructions.