A quantum-inspired approach to exploit turbulence structures

[1]  M. Cerezo,et al.  Variational quantum algorithms , 2020, Nature Reviews Physics.

[2]  C. Schwab,et al.  Deep neural network expression of posterior expectations in Bayesian PDE inversion , 2020, Inverse Problems.

[3]  S. Lloyd,et al.  Quantum algorithm for nonlinear differential equations , 2020, 2011.06571.

[4]  Andrew M. Childs,et al.  Efficient quantum algorithm for dissipative nonlinear differential equations , 2020, Proceedings of the National Academy of Sciences.

[5]  Marco Piñón.  I Overview , 2020, The Diaries and Letters of Lord Woolton 1940-1945.

[6]  A. Green,et al.  Real- and Imaginary-Time Evolution with Compressed Quantum Circuits , 2020, PRX Quantum.

[7]  Juan Jos'e Garc'ia-Ripoll,et al.  Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations , 2019, Quantum.

[8]  J. Joo,et al.  Variational quantum algorithms for nonlinear problems , 2019, Physical Review A.

[9]  Gerhard Wellein,et al.  Performance engineering for real and complex tall & skinny matrix multiplication kernels on GPUs , 2019, Int. J. High Perform. Comput. Appl..

[10]  M. Zaletel,et al.  Isometric Tensor Network States in Two Dimensions. , 2019, Physical review letters.

[11]  David A. Patterson,et al.  Motivation for and Evaluation of the First Tensor Processing Unit , 2018, IEEE Micro.

[12]  Dieter Jaksch,et al.  Multigrid renormalization , 2018, J. Comput. Phys..

[13]  Arash Nouri Gheimassi.  Self-Contained Filtered Density Function , 2018 .

[14]  Javier Jiménez,et al.  The turbulent cascade in five dimensions , 2017, Science.

[15]  Vassilios Theofilis,et al.  Modal Analysis of Fluid Flows: An Overview , 2017, 1702.01453.

[16]  Andrew M. Childs,et al.  Quantum Algorithm for Linear Differential Equations with Exponentially Improved Dependence on Precision , 2017, Communications in Mathematical Physics.

[17]  Sarah Al-Assam,et al.  The tensor network theory library , 2016, 1610.02244.

[18]  A. Chorin.  The Numerical Solution of the Navier-Stokes Equations for an Incompressible Fluid , 2015 .

[19]  Ivan V. Oseledets,et al.  Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation , 2015, SIAM J. Sci. Comput..

[20]  Yang Zhiyin,et al.  Large-eddy simulation: Past, present and the future , 2015 .

[21]  B. R. Noack.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 2013 .

[22]  Roman Orus,et al.  A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States , 2013, 1306.2164.

[23]  I. Oseledets.  Constructive Representation of Functions in Low-Rank Tensor Formats , 2012, Constructive Approximation.

[24]  Ivan V. Oseledets,et al.  Solution of Linear Systems and Matrix Inversion in the TT-Format , 2012, SIAM J. Sci. Comput..

[25]  G. Evenbly,et al.  Class of highly entangled many-body states that can be efficiently simulated. , 2012, Physical review letters.

[26]  Reinhold Schneider,et al.  On manifolds of tensors of fixed TT-rank , 2012, Numerische Mathematik.

[27]  Ivan Oseledets,et al.  Tensor-Train Decomposition , 2011, SIAM J. Sci. Comput..

[28]  F. Verstraete,et al.  Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space. , 2011, Physical review letters.

[29]  D. Huse,et al.  Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet , 2010, Science.

[30]  F. Verstraete,et al.  Simulations Based on Matrix Product States and Projected Entangled Pair States , 2010 .

[31]  Dominic W. Berry,et al.  High-order quantum algorithm for solving linear differential equations , 2010, ArXiv.

[32]  U. Schollwoeck.  The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[33]  Ors Legeza,et al.  Simulating strongly correlated quantum systems with tree tensor networks , 2010, 1006.3095.

[34]  J. Eisert,et al.  Colloquium: Area laws for the entanglement entropy , 2010 .

[35]  William E. Schiesser,et al.  Linear and nonlinear waves , 2009, Scholarpedia.

[36]  R. Mathis,et al.  Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers , 2009, Journal of Fluid Mechanics.

[37]  G. Evenbly,et al.  Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law , 2009, 0903.5017.

[38]  A. Harrow,et al.  Quantum algorithm for linear systems of equations. , 2008, Physical review letters.

[39]  J. Eisert,et al.  Area laws for the entanglement entropy - a review , 2008, 0808.3773.

[40]  F. Verstraete,et al.  Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , 2008, 0907.2796.

[41]  G. Eyink,et al.  Physical mechanism of the two-dimensional inverse energy cascade. , 2006, Physical review letters.

[42]  G. Vidal.  Entanglement renormalization. , 2005, Physical review letters.

[43]  G. Vidal,et al.  Classical simulation of quantum many-body systems with a tree tensor network , 2005, quant-ph/0511070.

[44]  G. Eyink.  Locality of turbulent cascades , 2005 .

[45]  D. Jaksch,et al.  Dynamics of the superfluid to Mott-insulator transition in one dimension (13 pages) , 2004, cond-mat/0405580.

[46]  S. Pope.  Ten questions concerning the large-eddy simulation of turbulent flows , 2004 .

[47]  Shengjun Wu,et al.  What is quantum entanglement , 2003 .

[48]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[49]  J. Shewchuk.  An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[50]  A. Kolmogorov,et al.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[51]  B. Fornberg.  Generation of finite difference formulas on arbitrarily spaced grids , 1988 .

[52]  S. Orszag,et al.  Small-scale structure of the Taylor–Green vortex , 1983, Journal of Fluid Mechanics.

[53]  G. S. Patterson,et al.  Numerical Simulation of Three-Dimensional Homogeneous Isotropic Turbulence , 1972 .

[54]  A. Fiacco.  Penalty methods for mathematical programming inEnwith general constraint sets , 1970 .

[55]  M. J. D. Powell,et al.  Nonlinear Programming—Sequential Unconstrained Minimization Techniques , 1969 .

[56]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[57]  J. Cole.  On a quasi-linear parabolic equation occurring in aerodynamics , 1951 .

[58]  E. Hopf.  The partial differential equation ut + uux = μxx , 1950 .

[59]  C. Weizsäcker.  Das Spektrum der Turbulenz bei großen Reynoldsschen Zahlen , 1948 .

[60]  W. Heisenberg,et al.  Zur statistischen Theorie der Turbulenz , 1948 .

[61]  H. Bateman,et al.  SOME RECENT RESEARCHES ON THE MOTION OF FLUIDS , 1915 .

[62]  Ivan Oseledets,et al.  Fast solution of multi-dimensional parabolic problems in the tensor train/quantized tensor train–format with initial application to the Fokker-Planck equation , 2012 .

[63]  D. Holdstock.  Past, present--and future? , 2005, Medicine, conflict, and survival.

[64]  Pierre Sagaut.  Large Eddy Simulation for Incompressible Flows. An Introduction , 2001 .

[65]  T. A. Zang,et al.  On the rotation and skew-symmetric forms for incompressible flow simulations , 1991 .

[66]  P. Givi.  Model-free simulations of turbulent reactive flows , 1989 .

[67]  S. Pope.  PDF methods for turbulent reactive flows , 1985 .

[68]  A. Hussain.  Coherent structures—reality and myth , 1983 .

[69]  F. Williams,et al.  Turbulent Reacting Flows , 1981 .

[70]  L. Onsager,et al.  Statistical hydrodynamics , 1949 .

[71]  J. Burgers.  A mathematical model illustrating the theory of turbulence , 1948 .