Related papers: Fourier transform of fermionic systems and the spe…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
Multi-dimensional Fourier transforms are key mathematical building blocks that appear in a wide range of applications from materials science, physics, chemistry and even machine learning. Over the past years, a multitude of software…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
We study the complexity of approximately contracting translation-invariant tensor networks. The computational cost of row-by-row tensor network contraction, which defines a discrete time evolution governed by a fixed transfer matrix, is…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…
We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because…
Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…
Stress and strain fields in a two-dimensional pixelwise disordered system are computed by a Fast Fourier Transform method. The system, a model for a ductile damaged medium, consists of an elastic-perfectly matrix containing void pixels. Its…
We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…
We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
Two methods for fast Fourier transforms are used in a quantum context. The first method is for systems with dimension of the Hilbert space $D=d^n$ with $d$ an odd integer, and is inspired by the Cooley-Tukey formalism. The `large Fourier…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…