# Quantum error correction and large $N$

@article{Milekhin2020QuantumEC,
title={Quantum error correction and large \$N\$},
author={Alexey Milekhin},
journal={SciPost Physics},
year={2020}
}
• A. Milekhin
• Published 28 August 2020
• Physics
• SciPost Physics
In recent years quantum error correction (QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large NN theories. Specifically we examine SU(N)SU(N) matrix quantum mechanics and 3-rank tensor O(N)^3O(N)3 theories. Both of these theories contain large gauge groups. We argue…
8 Citations

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## References

SHOWING 1-10 OF 61 REFERENCES

### Bulk locality and quantum error correction in AdS/CFT

• Physics
• 2014
A bstractWe point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the

### Spectra of eigenstates in fermionic tensor quantum mechanics

• Physics
Physical Review D
• 2018
We study the $O(N_1)\times O(N_2)\times O(N_3)$ symmetric quantum mechanics of 3-index Majorana fermions. When the ranks $N_i$ are all equal, this model has a large $N$ limit which is dominated by

### Continuous Symmetries and Approximate Quantum Error Correction

• Computer Science
Physical Review X
• 2020
The approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and the five-rotor code can be stacked to form a covariant holographic code.

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

• Computer Science
• 2015
That bulk logical operators can be represented on multiple boundary regions mimics the Rindlerwedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in [1].

### Large N limits as classical mechanics

This paper discusses the sense in which the large $N$ limits of various quantum theories are equivalent to classical limits. A general method for finding classical limits in arbitrary quantum

### The Ryu–Takayanagi Formula from Quantum Error Correction

I argue that a version of the quantum-corrected Ryu–Takayanagi formula holds in any quantum error-correcting code. I present this result as a series of theorems of increasing generality, with the

### Scrambling and decoding the charged quantum information

Some deep conjectures about quantum gravity are closely related to the role of symmetries in the gravitational background, especially for quantum black holes. In this paper, we systematically study

### Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality.

• Physics
Physical review letters
• 2016
In this Letter we prove a simple theorem in quantum information theory, which implies that bulk operators in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence can be reconstructed as

### Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models

• Mathematics
• 2017
Certain models with rank-$3$ tensor degrees of freedom have been shown by Gurau and collaborators to possess a novel large $N$ limit, where $g^2 N^3$ is held fixed. In this limit the perturbative