# Tensor network models of AdS/qCFT

@article{Jahn2022TensorNM, title={Tensor network models of AdS/qCFT}, author={Alexander Jahn and Zolt'an Zimbor'as and Jens Eisert}, journal={Quantum}, year={2022}, volume={6}, pages={643} }

The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. To reproduce various features of AdS/CFT, a large number of discrete models based on tensor networks have been proposed. Some recent models, most notably including toy models of holographic quantum error…

## 12 Citations

### Boundary theories of critical matchgate tensor networks

- Computer ScienceJournal of High Energy Physics
- 2022

This work substantially sharpen the relationship between AdS/CFT correspondence and tensor networks on regular hyperbolic tilings by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging.

### Path integral optimization from Hartle-Hawking wave function

- Physics
- 2021

We propose a gravity dual description of the path-integral optimization in conformal field theories arXiv:1703.00456, using Hartle-Hawking wave functions in anti-de Sitter spacetimes. We show that…

### Conformal properties of hyperinvariant tensor networks

- Computer ScienceScientific reports
- 2022

This manuscript analyzes the challenges related to optimizing tensors in a hyMERA with respect to some quasiperiodic critical spin chain, and compares with standard approaches in MERA, and shows two new sets of tensor decompositions which exhibit different properties from the original construction.

### Holographic tensor network models and quantum error correction: a topical review

- PhysicsQuantum Science and Technology
- 2021

Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A…

### Holography, cellulations and error correcting codes

- Computer Science
- 2021

This paper constructs analogues of the HaPPY code for three-dimensional hyperbolic space (AdS4), using both absolutely maximally entangled (AME) and non-AME codes, and explains how these codes could be applied to interesting classes of holographic dualities based on gravity-scalar theories through toroidal reductions ofhyperbolic spaces.

### Holographic path-integral optimization

- PhysicsJournal of High Energy Physics
- 2021

Abstract
In this work we elaborate on holographic description of the path-integral optimization in conformal field theories (CFT) using Hartle-Hawking wave functions in Anti-de Sitter spacetimes. We…

### Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations

- Computer Science
- 2021

This work provides guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation functions, and provides an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.

### Understanding holographic error correction via unique algebras and atomic examples

- Computer ScienceJournal of High Energy Physics
- 2022

A fully constructive characterisation of holographic quantum error-correcting codes is introduced, given a code and an erasure error, and the uniqueness of the algebra satisfying complementary recovery is proved.

### Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks

- Computer SciencePRX Quantum
- 2022

A flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states in a modular fashion, generalizing code concatenation.

### Parallel decoding of multiple logical qubits in tensor-network codes

- Computer SciencePhysical Review A
- 2022

It is shown that, by using the parallel decoding scheme, the complexity is also linear in k, the number of logical qubits, which allows us to exactly contract tensor networks corresponding to codes with up to half a million qubits.

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