Related papers: Simulating Quantum Turbulence with Matrix Product …
Static disorder plays a crucial role in the electronic dynamics and spectroscopy of complex molecular systems. Traditionally, obtaining observables averaged over static disorder requires thousands of realizations via direct sampling of the…
There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
We consider the class of dual-unitary quantum circuits in $1+1$ dimensions and introduce a notion of ``solvable'' matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We…
Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…
This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…
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…
We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that…
Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or…
Using direct numerical simulations (DNSs), the interaction between linear waves and turbulence under the compressible magnetohydrodynamic (CMHD) approach was studied. A set of DNSs in three dimensions for a spatial resolution of $128^3$ and…
Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are…
The evolution of a turbulent tangle of quantum vortices in presence of finite-size active particles is studied by means of numerical simulations of the Gross-Pitaevskii equation. Particles are modeled as potentials depleting the superfluid…
We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$ grid points. The…
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
Evaluating quantum algorithms at utility-scale - involving more than 100 qubits - is a key step toward advancing real-world applications of quantum computing. In this study, we benchmark seven state-of-the-art quantum emulators employing…
Matrix Product State (MPS) is a versatile tensor network representation widely applied in quantum physics, quantum chemistry, and machine learning, etc. MPS sampling serves as a critical fundamental operation in these fields. As the…