Related papers: Learning with errors may remain hard against quant…
We study the \textit{entanglement contour} and \textit{partial entanglement entropy} (PEE) in quantum field theories in 3 and higher dimensions. The entanglement entropy is evaluated from a certain limit of the PEE with a geometric…
Knowledge graph embedding (KGE) has shown great potential in automatic knowledge graph (KG) completion and knowledge-driven tasks. However, recent KGE models suffer from high training cost and large storage space, thus limiting their…
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations. These…
Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…
We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms we…
Holographic Conformal Field Theories (CFTs) are usually studied in a limit where the gravity description is weakly coupled. By contrast, lattice quantum field theory can be used as a tool for doing computations in a wider class of…
This dissertation represents work on three different subjects relating to quantum gravity and the AdS/CFT correspondence. First, we review a holographic computation of the one-loop corrections to the Weyl anomaly on Ricci flat backgrounds…
A deep learning system typically suffers from a lack of reproducibility that is partially rooted in hardware or software implementation details. The irreproducibility leads to skepticism in deep learning technologies and it can hinder them…
This is an extended version of our short report hep-th/0603001, where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
We consider the second R\'enyi entropy $S^{(2)}$ in pure lattice gauge theory with $SU(2)$, $SU(3)$ and $SU(4)$ gauge groups, which serves as a first approximation for the entanglement entropy and the entropic $C$-function. We compare the…
We present a strategy for the quantum simulation of many-body lattice models with constrained Hilbert spaces. We focus on lattice gauge theories (LGTs), which underlie a wide range of phenomena in particle physics, condensed matter, and…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
We discuss the computation of holographic entanglement entropy for interface conformal field theories. The fact that globally well defined Fefferman-Graham coordinates are difficult to construct makes the regularization of the holographic…
We propose a holographic model for local quench in 1+1 dimensional Conformal Field Theory (CFT). The local quench is produced by joining two identical CFT's on semi-infinite lines. When these theories have a zero boundary entropy, we use…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
The Kitaev surface-code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
We introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous…
The number of measurements demanded by hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) is prohibitively high for many problems of practical value. For such problems, realizing quantum advantage will…