Quantum error correction and large $N$

Milekhin, Alexey

doi:10.21468/SciPostPhys.11.5.094

SciPost Physics

Quantum error correction and large $N$

Alexey Milekhin

SciPost Phys. 11, 094 (2021) · published 19 November 2021

doi: 10.21468/SciPostPhys.11.5.094
pdf
Submissions/Reports

Abstract

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.11.5.094
TI  - Quantum error correction and large $N$
PY  - 2021/11/19
UR  - https://www.scipost.org/SciPostPhys.11.5.094
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 11
IS  - 5
SP  - 094
A1  - Milekhin, Alexey
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.11.5.094,
	title={{Quantum error correction and large $N$}},
	author={Alexey Milekhin},
	journal={SciPost Phys.},
	volume={11},
	pages={094},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.11.5.094},
	url={https://scipost.org/10.21468/SciPostPhys.11.5.094},
}

Cited by 3

Author / Affiliation: mappings to Contributors and Organizations

See all Organizations.

¹ Alexey Milekhin

¹ Princeton University