Related papers: Hyper-invariant tensor networks and holography
We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multi-scale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator,…
Discrete models of holographic dualities, typically modeled by tensor networks on hyperbolic tilings, produce quantum states with a characteristic quasiperiodic disorder not present in continuum holography. In this work, we study the…
The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes…
We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to…
Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg…
In this paper, we introduce a tensor network (TN) scheme into the entanglement augmentation process of the synergistic optimization framework by Rudolph et al. [arXiv:2208.13673] to build its process systematically for inhomogeneous…
In a recent contribution [arXiv:0904:4151] entanglement renormalization was generalized to fermionic lattice systems in two spatial dimensions. Entanglement renormalization is a real-space coarse-graining transformation for lattice systems…
We use the multiscale entanglement renormalisation ansatz (MERA) to numerically investigate three critical quantum spin chains with Z_2 x Z_2 on-site symmetry: a staggered XXZ model, a transverse field cluster model, and the quantum…
In tensor networks, a geometric operation of pushing a bond cut surface toward a minimal surface corresponds to entanglement distillation. Cutting bonds defines a reduced transition matrix on the bond cut surface and the associated quantum…
In 1+1-dimensional conformal field theory, the thermal state on a circle is related to a certain quotient of the vacuum on a line. We explain how to take this quotient in the MERA tensor network representation of the vacuum and confirm the…
We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…
Understanding the limiting capabilities of classical methods in simulating complex quantum systems is of paramount importance for quantum technologies. Although many advanced approaches have been proposed and recently used to challenge…
Exponential regularization of orthogonal and Anti-de Sitter (AdS) space is presented based on noncommutative geometry. We show that an adequately adopted noncommutative deformation of geometry makes the holography of higher dimensional…
The AdS/CFT correspondence realises the holographic principle where information in the bulk of a space is encoded at its border. We are yet a long way from a full mathematical construction of AdS/CFT, but toy models in the form of…
We discuss a one-parameter family of states in two-dimensional holographic conformal field theories which are constructed via the Euclidean path integral of an effective theory on a family of hyperbolic slices in the dual bulk geometry. The…
The multi-scale entanglement renormalization ansatz (MERA) provides a natural description of the ground state of a quantum critical Hamiltonian on the lattice. From an optimized MERA, one can extract the scaling dimensions of the underlying…
We investigate whether a multiscale tensor-network architecture can provide a useful inductive bias for reconstruction-based anomaly detection in collider jets. Jets are produced by a branching cascade, so their internal structure is…
Continuous tensor networks are variational wavefunctions proposed in recent years to efficiently simulate quantum field theories (QFTs). Prominent examples include the continuous matrix product state (cMPS) and the continuous multi-scale…
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the…
Entanglement renormalization circuits are quantum circuits that can be used to prepare large-scale entangled states. For years, it has remained a mystery whether there exist scale-invariant entanglement renormalization circuits for chiral…