A Quantum Inspired Approach to Exploit Turbulence Structures

Abstract

Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in space and time. Here we introduce a new paradigm for analyzing the structure of turbulent flows by quantifying correlations between different length scales using methods inspired from quantum many-body physics. We present results for interscale correlations of two paradigmatic flow examples, and use these insights along with tensor network theory to design a structure-resolving algorithm for simulating turbulent flows. With this algorithm, we find that the incompressible Navier-Stokes equations can be accurately solved within a computational space reduced by over an order of magnitude compared to direct numerical simulation. Our quantum-inspired approach provides a pathway towards conducting computational fluid dynamics on quantum computers.

Newest and final version of our article

References in corpus (5)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• The turbulent cascade in five dimensions
• Quantum algorithm for nonlinear differential equations

Cited by in corpus (61)

• Variational Quantum Algorithms for Computational Fluid Dynamics
• Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation
• Hybrid quantum-classical reservoir computing of thermal convection flow
• Quantum Fourier Transform Has Small Entanglement
• Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
• Variational Quantum Solutions to the Advection-Diffusion Equation for Applications in Fluid Dynamics
• Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
• Hybrid quantum algorithms for flow problems
• Learning tensor networks with tensor cross interpolation: new algorithms and libraries
• Efficient quantum amplitude encoding of polynomial functions
• Complete quantum-inspired framework for computational fluid dynamics
• Density Matrix Renormalization Group with Tensor Processing Units
• Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes
• A quantum-inspired method for solving the Vlasov-Poisson equations
• Variational Quantum Evolution Equation Solver
• Gauging tensor networks with belief propagation
• Two quantum algorithms for solving the one-dimensional advection-diffusion equation
• Tensor networks enable the calculation of turbulence probability distributions
• Nonlinear dynamics as a ground-state solution on quantum computers
• Tensor network reduced order models for wall-bounded flows
• Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation
• Simulating unsteady fluid flows on a superconducting quantum processor
• Simulating fluid flows with quantum computing
• Quantum algorithms for scientific computing
• Two-particle calculations with quantics tensor trains: Solving the parquet equations
• Quantum-Inspired Fluid Simulation of 2D Turbulence with GPU Acceleration
• Quantized tensor networks for solving the Vlasov-Maxwell equations
• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• Compactness of quantics tensor train representations of local imaginary-time propagators
• Functional Tensor Network Solving Many-body Schrödinger Equation
• Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models
• Tensorized orbitals for computational chemistry
• Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method
• Implementation of spectral methods on Ising machines: toward flow simulations on quantum annealer
• Quantum computing for simulation of fluid dynamics
• Quantum Dynamics Simulation of the Advection-Diffusion Equation
• The turbulence development at its initial stage: a scenario based on the idea of vortices decay
• Learning parameter dependence for Fourier-based option pricing with tensor trains
• The system of the vortex-like structures: the viewpoint on a turbulence modelling
• Direct interpolative construction of the discrete Fourier transform as a matrix product operator
• Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains
• Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics
• Survey on Computational Applications of Tensor Network Simulations
• Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
• Tensor-Programmable Quantum Circuits for Solving Differential Equations
• Adaptive sampling-based optimization of quantics tensor trains for noisy functions: applications to quantum simulations
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks
• Typical Machine Learning Datasets as Low-Depth Quantum Circuits
• An Efficient Decomposition of the Carleman Linearized Burgers' Equation
• Simulating Quantum Turbulence with Matrix Product States
• Pseudospectral method for solving PDEs using Matrix Product States
• Inchworm tensor train hybridization expansion quantum impurity solver
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• AC/DC spin current in ferromagnet/superconductor/normal metal trilayer systems
• Formulation and evaluation of ocean dynamics problems as optimization problems for quantum annealing machines
• Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Vortex Detection from Quantum Data
• Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation