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Related papers: Consistency Conditions for an AdS/MERA Corresponde…

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The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA…

Strongly Correlated Electrons · Physics 2008-02-22 Miguel Aguado , Guifre Vidal

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…

Neural and Evolutionary Computing · Computer Science 2018-12-14 Andrew Hallam , Edward Grant , Vid Stojevic , Simone Severini , Andrew G. Green

We propose a symmetric version of the multi-scale entanglement renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this Ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising…

Other Condensed Matter · Physics 2016-09-08 Lukasz Cincio , Jacek Dziarmaga , Marek M. Rams

The holographic duality relates a field theory to a theory of (quantum) gravity in one dimension more. The extra dimension represents the scale of the RG transformation in the field theory. It has been conjectured that the tensor networks…

Strongly Correlated Electrons · Physics 2015-10-29 Johannes M. Oberreuter , Stefan Kehrein

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…

Quantum Physics · Physics 2012-03-02 G. Evenbly , G. Vidal

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum…

Strongly Correlated Electrons · Physics 2010-11-02 G. Evenbly , R. N. C. Pfeifer , V. Pico , S. Iblisdir , L. Tagliacozzo , I. P. McCulloch , G. Vidal

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one…

Quantum Physics · Physics 2010-07-16 Thomas Barthel , Martin Kliesch , Jens Eisert

The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the…

High Energy Physics - Theory · Physics 2021-09-21 Jose J. Fernandez-Melgarejo , Javier Molina-Vilaplana

We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do…

High Energy Physics - Theory · Physics 2015-07-15 Masamichi Miyaji , Tadashi Takayanagi

Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT…

High Energy Physics - Theory · Physics 2016-11-07 Patrick Hayden , Sepehr Nezami , Xiao-Liang Qi , Nathaniel Thomas , Michael Walter , Zhao Yang

Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce…

High Energy Physics - Theory · Physics 2016-03-23 Zhao Yang , Patrick Hayden , Xiao-Liang Qi

The continuous Multiscale Entanglement Renormalization Ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)] gives a variational wavefunctional for ground states of quantum field theoretic Hamiltonians. A cMERA is defined as…

Quantum Physics · Physics 2021-09-29 Adrián Franco-Rubio

We describe a quantum circuit that produces a highly entangled state of N qubits from which one can efficiently compute expectation values of local observables. This construction yields a variational ansatz for quantum many-body states that…

Quantum Physics · Physics 2014-06-25 Glen Evenbly , Guifre Vidal

We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal…

High Energy Physics - Theory · Physics 2015-07-23 Fernando Pastawski , Beni Yoshida , Daniel Harlow , John Preskill

We derive the multiscale entanglement renormalization ansatz (MERA) for the single impuity Kondo model. We find two types of hidden quantum entanglement: one comes from a finite-temperature effect on the geometry of the MERA network, and…

Statistical Mechanics · Physics 2012-08-15 Hiroaki Matsueda

We demonstrate, in the context of quadratic fermion lattice models in one and two spatial dimensions, the potential of entanglement renormalization (ER) to define a proper real-space renormalization group transformation. Our results show,…

Quantum Physics · Physics 2015-05-13 G. Evenbly , G. Vidal

We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and…

Strongly Correlated Electrons · Physics 2015-11-18 Glen Evenbly , Guifre Vidal

Hyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence.…

Quantum Physics · Physics 2023-11-14 Matthew Steinberg , Javier Prior

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete…

Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but…

Strongly Correlated Electrons · Physics 2010-10-01 Robert N. C. Pfeifer , Philippe Corboz , Oliver Buerschaper , Miguel Aguado , Matthias Troyer , Guifre Vidal