# Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence

@article{Pastawski2015HolographicQE, title={Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence}, author={Fernando Pastawski and Beni Yoshida and Daniel Harlow and John Preskill}, journal={Journal of High Energy Physics}, year={2015}, volume={2015}, pages={1-55} }

A bstractWe propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom…

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Abstract
We first show that a class of operators acting on a given bipartite pure state on ℋ
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⊗ ℋ
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⊗ ℋ
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to only ℋ
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or ℋ
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