Related papers: Simulating Quantum Turbulence with Matrix Product …
Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…
We performed numerical simulations of decaying quantum turbulence by using a generalized Gross-Pitaevskii equation, that includes a beyond mean field correction and a nonlocal interaction potential. The nonlocal potential is chosen in order…
Two-way coupled DNS simulation of particle-laden turbulent Couette-flow [1], in the volume fraction regime $\phi>10^{-4}$, showed a discontinuous decrease of turbulence intensity beyond a critical volume fraction…
The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this…
We investigate the fluid-solid interaction of suspensions of Kolmogorov-size spherical particles moving in homogeneous isotropic turbulence at a microscale Reynolds number of $Re_\lambda \approx 140$. Two volume fractions are considered,…
Simulation of turbulent flows at high Reynolds number is a computationally challenging task relevant to a large number of engineering and scientific applications in diverse fields such as climate science, aerodynamics, and combustion.…
We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are,…
We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent…
As neural networks are known to efficiently represent classes of tensor-network states as well as volume-law-entangled states, identifying which properties determine the representational capabilities of neural quantum states (NQS) remains…
Tensor Processing Units (TPUs) were developed by Google exclusively to support large-scale machine learning tasks. TPUs can, however, also be used to accelerate and scale up other computationally demanding tasks. In this paper we repurpose…
Simulating nonlinear partial differential equations (PDEs) such as the Navier--Stokes (NS) equations remains computationally intensive, especially when implicit time integration is used to capture multiscale flow dynamics. This work…
We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…
This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body…
The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with…
This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method…
Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices where each physical degree of freedom is associated to an environment degree of freedom. MPDOs have interesting properties for…
We study the statistics of velocity circulation in two-dimensional classical and quantum turbulence. We perform numerical simulations of the incompressible Navier-Stokes and the Gross-Pitaevskii (GP) equations for the direct and inverse…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…