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We propose a numerical method for kinetic plasma simulation in which the phase-space distribution function is represented by a low-rank tensor network with an adaptive level of compression. The Vlasov-Poisson system is advanced using Strang…
Modern Neural Networks are eminent in achieving state of the art performance on tasks under Computer Vision, Natural Language Processing and related verticals. However, they are notorious for their voracious memory and compute appetite…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
The configuration interaction (CI) is a versatile wavefunction theory for interacting fermions but it involves an extremely long CI series. Using a symmetric tensor decomposition (STD) method, we convert the CI series into a compact and…
The outstanding performance of large foundational models across diverse tasks, from computer vision to speech and natural language processing, has significantly increased their demand. However, storing and transmitting these models poses…
In systems undergoing localization-delocalization quantum phase transitions due to disorder or monitoring, there is a crucial need for robust methods capable of distinguishing phases and uncovering their intrinsic properties. In this work,…
A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…
Convolutional neural networks are now seeing widespread use in a variety of fields, including image classification, facial and object recognition, medical imaging analysis, and many more. In addition, there are applications such as…
There are quasi-conformal theories, like the Minimal and Ultraminimal Technicolor models, which may break dynamically the gauge symmetry of the Standard Model and at the same time are compatible with electroweak precision data. The main…
The recently proposed excitonic renormalization framework presents an alternative ansatz to elec- tronic structure theory of weakly interacting fragments. It makes use of absolutely localized orbitals and correlated states evaluated on…
Deep learning techniques have opened a new venue for electronic structure theory in recent years. In contrast to traditional methods, deep neural networks provide much more expressive and flexible wave function ansatz, resulting in better…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…
In this work, we propose a technique for the use of fermionic neural networks (FermiNets) with the Slater exponential Ansatz for electron-nuclear and electron-electron distances, which provides faster convergence of target ground-state…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
We derive a powerful yet simple method for analyzing the local density of states in gapless one dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the…
Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…
We investigate the physics of projected d-wave pairing states using their fermionic projected entangled pair state (fPEPS) representation. First, we approximate a d-wave Bardeen-Cooper-Schrieffer state using the Gaussian fPEPS. Next, we…
We present a comprehensive pedagogical introduction to the dimensional reduction protocol (DRP), a versatile framework for analyzing instabilities and critical points in interacting fermionic systems. The DRP simplifies the study of…