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The AdS/CFT correspondence is a realization of the holographic principle in the context of string theory. It is a map between a quantum field theory and a string theory living in one or more extra dimensions. Holography provides new tools…
We introduce a holographic framework for analyzing the steady states of repeated quantum channels with strong symmetries. Using channel-state duality, we show that the steady state of a $d$-dimensional quantum channel is holographically…
The holographic principle suggests that the low energy effective field theory of gravity, as used to describe perturbative quantum fields about some background has far too many states. It is then natural that any quantum error correcting…
We investigate the formation of topological defects in the course of a dynamical phase transition with different boundary conditions in a ring from AdS/CFT correspondence. According to the Kibble-Zurek mechanism, quenching the system across…
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 present a deep neural network representation of the AdS/CFT correspondence, and demonstrate the emergence of the bulk metric function via the learning process for given data sets of response in boundary quantum field theories. The…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint. The framework rests on three…
We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the two…
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
The Multi-scale Entanglement Renormalization Ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of…
At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing…
We construct operators in holographic two-dimensional conformal field theory, which act locally in the code subspace as arbitrary bulk spacelike vector fields. Key to the construction is an interplay between parallel transport in the bulk…
It is well-known that the entanglement entropies for spacelike subregions, and the associated modular Hamiltonians play a crucial role in the bulk reconstruction program within Anti de-Sitter (AdS) holography. Explicit examples of HKLL map…
In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In…
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an…
We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate…
Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ``background entanglement'', i.e. links of a fixed state,…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
This paper systematically develops the concept of entanglement threads that characterize the entanglement structure of holographic duality. Behind this framework lies a simple philosophy: holographic quantum entanglement can be visualized…