Related papers: A Simple and General Equation for Matrix Product U…

In this manuscript, we present a common tensor framework which can be used to generalize one-dimensional numerical tasks to arbitrary dimension $d$ by means of tensor product formulas. This is useful, for example, in the context of…

This paper presents a broad, pathfinding design space exploration of memory management units (MMUs) for heterogeneous systems. We consider a variety of designs, ranging from accelerators tightly coupled with CPUs (and using their MMUs) to…

Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…

Neutrino telescopes are opening new opportunities in observational high energy astrophysics. In these detectors, atmospheric muons from primary cosmic ray interactions in the atmosphere play an important role. They provide the most abundant…

We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent iid random matrices, as $M$ is fixed, and the sizes of the matrices tend to infinity. This…

While recent advances in AI SoC design have focused heavily on accelerating tensor computation, the equally critical task of tensor manipulation, centered on high,volume data movement with minimal computation, remains underexplored. This…

We present the explicit expressions for the matrix product operator (MPO) representation for the local conserved quantities of the Heisenberg chain. The bond dimension of the MPO grows linearly with the locality of the charges. The MPO has…

We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection property ensures that the ground space consists of MPS, with…

In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…

As a method beyond the mean-field analysis, a matrix product state (MPS) with incommensurate periodicity is applied to detect phase transitions accompanied with periodicity change, where the incommensurate MPS is generated by acting…

We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the…

Running machine learning inference on tiny devices, known as TinyML, is an emerging research area. This task requires generating inference code that uses memory frugally, a task that standard ML frameworks are ill-suited for. A deployment…

The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…

Matrix-product states (MPS) have proven to be a versatile ansatz for modeling quantum many-body physics. For many applications, and particularly in one-dimension, they capture relevant quantum correlations in many-body wavefunctions while…

This paper introduces Multidimensional Task Learning (MTL), a unified mathematical framework based on Generalized Einstein MLPs (GE-MLPs) that operate directly on tensors via the Einstein product. We argue that current computer vision task…

The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find…

The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…

Direct numerical simulation (DNS) of turbulent reactive flows has been the subject of significant research interest for several decades. Accurate prediction of the effects of turbulence on the rate of reactant conversion, and the subsequent…

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple…

Phasor Measurement Units (PMUs) are measurement devices long used in transmission systems and today even more essential for a proper monitoring of distribution grids. The expected massive penetration of distributed energy resources (DERs)…