# Quantum error correction and large $N$

@article{Milekhin2020QuantumEC, title={Quantum error correction and large \$N\$}, author={Alexey Milekhin}, journal={SciPost Physics}, year={2020} }

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

### Quantum stabilizer codes, lattices, and CFTs

- Computer ScienceArXiv
- 2020

It is shown that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs, and thus Narain C FTs are defined.

### Toward simulating superstring/M-theory on a quantum computer

- PhysicsJournal of High Energy Physics
- 2021

Abstract
We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in…

### Overcounting of interior excitations: a resolution to the bags of gold paradox in AdS

- Physics
- 2020

In this work, we investigate how single-sided and eternal black holes in AdS can host an enormous number of semiclassical excitations in their interior, which is seemingly not reflected in the…

### Many-Body Scars as a Group Invariant Sector of Hilbert Space.

- MathematicsPhysical review letters
- 2020

A class of Hamiltonians H for which a sector of the Hilbert space invariant under a Lie group G, which is not a symmetry of H, possesses the essential properties of many-body scar states, which could be used for reliable quantum information processing.

### All-orders asymptotics of tensor model observables from symmetries of restricted partitions

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

The counting of the dimension of the space of U(N)×U(N)×U(N) polynomial invariants of a complex 3-index tensor as a function of degree n is known in terms of a sum of squares of Kronecker…

### Large $N$ Matrix Quantum Mechanics as a Quantum Memory

- Physics
- 2022

In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large N matrix quantum mechanics models. First, we investigate the gauged SU ( N ) matrix…

### Quantum error correction in SYK and bulk emergence

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We analyze the error correcting properties of the Sachdev-Ye-Kitaev model, with errors that correspond to erasures of subsets of fermions. We study the limit where the number of fermions…

### Optimal universal quantum error correction via bounded reference frames

- PhysicsPhysical Review Research
- 2022

Yuxiang Yang,1, 2 Yin Mo,2 Joseph M. Renes,1 Giulio Chiribella,2, 3, 4, 5 and Mischa P. Woods1 Institute for Theoretical Physics, ETH Zürich, Switzerland QICI Quantum Information and Computation…

## 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

- PhysicsPhysical 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 SciencePhysical 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

- Physics
- 1982

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

- Mathematics
- 2016

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

- PhysicsPhysical Review Research
- 2020

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.

- PhysicsPhysical 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…