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We develop a statistically robust framework for reconstructing metal--semiconductor contact regions using topological gradients. The inverse problem is formulated as the identification of an unknown contact region from boundary measurements…

Recent advances in quantum computing devices have brought attention to hybrid quantum-classical algorithms like the Variational Quantum Eigensolver (VQE) as a potential route to practical quantum advantage in chemistry. However, it is not…

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and…

Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures.…

As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a…

The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…

In this letter, we develop a unified semiclassical framework for the thermodynamics and quantization of the Reissner--Nordstr\"om (RN) black hole (BH) based on the Misner--Sharp--Hernandez (MSH) mass. Treating the quasi-local horizon…

Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become…

Holographic methods are used to investigate the low temperature limit, including quantum critical behavior, of strongly coupled 4-dimensional gauge theories in the presence of an external magnetic field, and finite charge density. In…

Circuit optimization is a fundamental task for practical applications of near-term quantum computers. In this work we address this challenge through the powerful lenses of tensor network theory. Our approach involves the full…

Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…

We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations,…

Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We…

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated…

An algorithm for optimizing the MERA tensor network in an infinite system is presented. Using this technique we compute the critical exponents of Ising and XXZ model.

We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient…

Quantum computing architectures require an accurate and efficient description in terms of many-electron states. Recent implementations include quantum dot arrays, where the ground state of a multi q-bit system can be altered by voltages…

In this paper, we study the numerical method for the bi-Laplace problems with inhomogeneous coefficients; particularly, we propose finite element schemes on rectangular grids respectively for an inhomogeneous fourth-order elliptic singular…

We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and…