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Kelvin-Helmholtz instability

Dr Nikita Gourianov

Research Scientist

Sub department

  • Atomic and Laser Physics

Research groups

  • Quantum systems engineering
nikita.gourianov@physics.ox.ac.uk
Clarendon Laboratory, room Old Library
  • About
  • Publications

Tensor networks enable the calculation of turbulence probability distributions

Science Advances, Vol 11, Issue 5, 2025

Authors:

Nikita Gourianov, Peyman Givi, Dieter Jaksch, Stephen B Pope

Abstract:

A quantum-inspired approach to exploit turbulence structures

Nature Computational Science Springer Nature 2:2022 (2022) 30-37

Authors:

Nikita Gourianov, Michael Lubasch, Sergey Dolgov, van den Berg Quincy Yves, Hessam Babaee, Peyman Givi, Martin Kiffner, Dieter Jaksch

Abstract:

Understanding turbulence is key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multiscale nature, describing the coupling between different-sized eddies in space and time. Here we analyze the structure of turbulent flows by quantifying correlations between different length scales using methods inspired from quantum many-body physics. We present the 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 even when reducing the number of parameters required to represent the velocity field by more than one order of magnitude compared to direct numerical simulation. Our quantum-inspired approach provides a pathway towards conducting computational fluid dynamics on quantum computers.
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Parallel time-dependent variational principle algorithm for matrix product states

PHYSICAL REVIEW B 101:23 (2020) ARTN 235123

Authors:

Paul Secular, Nikita Gourianov, Michael Lubasch, Sergey Dolgov, Stephen R Clark, Dieter Jaksch

Abstract:

© 2020 American Physical Society. ©2020 American Physical Society. Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving one-dimensional (1D) quantum lattice systems with long-range interactions. We benchmark the accuracy and performance of the algorithm by simulating quenches in the long-range Ising and XY models. We show that our code scales well up to 32 processes, with parallel efficiencies as high as 86%. Finally, we calculate the dynamical correlation function of a 201-site Heisenberg XXX spin chain with 1/r2 interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex many-body systems.
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Dynamical Regularities of US Equities Opening and Closing Auctions

Market Microstructure and Liquidity World Scientific Pub Co Pte Lt (2019) 1950001-1950001

Authors:

Damien Challet, Nikita Gourianov
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Tensor networks enable the calculation of turbulence probability distributions

(2024)

Authors:

Nikita Gourianov, Peyman Givi, Dieter Jaksch, Stephen B Pope
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