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Quantum error correction and large $N$

by Alexey Milekhin

Submission summary

As Contributors: Alexey Milekhin
Arxiv Link: (pdf)
Date submitted: 2021-07-17 01:14
Submitted by: Milekhin, Alexey
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


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 $N$ theories. Specifically we examine $SU(N)$ matrix quantum mechanics and 3-rank tensor $O(N)^3$ theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large $N$ analysis and do not appeal to a particular form of Hamiltonian or holography.

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Submission 2008.12869v2 on 17 July 2021

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