Fetching the paper…
Reading the bibliography…
We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity.
Hamiltonian systems and transformation in hilbert space
Bernard O Koopman · 1931
Earlier work this paper cites.
Zur operatorenmethode in der klassischen mechanik
John von Neumann · 1932
Earlier work this paper cites.
Nonlinear dynamical systems and classical orthogonal polynomials
Krzysztof Kowalski · 1997
Earlier work this paper cites.
Nonlinear quantum mechanics implies polynomial-time solution for np-complete and #p problems
Daniel S Abrams and Seth Lloyd · 1998
Earlier work this paper cites.
Kolmogorov equation associated to a stochastic Navier–Stokes equation
Franco Flandoli and Fausto Gozzi · 1998
Earlier work this paper cites.
Special functions , volume 71
George E Andrews, Richard Askey, Ranjan Roy, Ranjan Roy, and Richard Askey · 1999
Earlier work this paper cites.
Navier-Stokes Equations and Turbulence
C. Foias, O. Manley, R. Rosa, and R. Temam · 2001
Earlier work this paper cites.
Classical and quantum computation
Alexei Yu Kitaev, Alexander Shen, and Mikhail N Vyalyi · 2002
Earlier work this paper cites.
Creating superpositions that correspond to efficiently integrable probability distributions
Lov Grover and Terry Rudolph · 2002
Earlier work this paper cites.
The Theory of Stochastic Processes: I , volume 210
Iosif I Gikhman and Anatoli V Skorokhod · 2004
Earlier work this paper cites.
Kolmogorov equations for stochastic PDEs
Giuseppe Da Prato · 2004
Earlier work this paper cites.
Transformation of quantum states using uniformly controlled rotations
Mikko Mottonen, Juha J Vartiainen, Ville Bergholm, and Martti M Salomaa · 2004
Earlier work this paper cites.
Ergodicity of the 2d Navier–Stokes equations with degenerate stochastic forcing
Martin Hairer and Jonathan C Mattingly · 2006
Earlier work this paper cites.
Infinite-dimensional parabolic equations in Gauss-Sobolev spaces
Pao-Liu Chow · 2007
Earlier work this paper cites.
A quantum algorithm to solve nonlinear differential equations
Sarah K Leyton and Tobias J Osborne · 2008
Earlier work this paper cites.
Stochastic differential equations: an introduction with applications
Bernt Oksendal · 2013
Earlier work this paper cites.
Exponential improvement in precision for simulating sparse hamiltonians
Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma · 2014
Cited alongside, same era.
Stochastic Analysis: A Series of Lectures
Robert C Dalang, Marco Dozzi, Franco Flandoli, and Francesco Russo · 2015
Cited alongside, same era.
Complexity-theoretic foundations of quantum supremacy experiments
Scott Aaronson and Lijie Chen · 2016
Cited alongside, same era.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
Andrew M Childs and Joshua Young · 2016
Cited alongside, same era.
Optimal hamiltonian simulation by quantum signal processing
Guang Hao Low and Isaac L Chuang · 2017
Cited alongside, same era.
Quantum signal processing by single-qubit dynamics
A variational quantum algorithm for the feynman-kac formula
Hedayat Alghassi, Amol Deshmukh, Noelle Ibrahim, Nicolas Robles, Stefan Woerner, and Christa Zoufal · 2022
Later among the works it cites.
Yu Tanaka and Keisuke Fujii · 2023
Later among the works it cites.
Koopman spectral linearization vs. carleman linearization: A computational comparison study
Dongwei Shi and Xiu Yang · 2023
Later among the works it cites.
A polynomial-time classical algorithm for noisy random circuit sampling
Dorit Aharonov, Xun Gao, Zeph Landau, Yunchao Liu, and Umesh Vazirani · 2023
Later among the works it cites.
From optimization to sampling through gradient flows
N García Trillos, Bamdad Hosseini, and Daniel Sanz-Alonso · 2023
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Guang Hao Low · 2017
Cited alongside, same era.
A detectability criterion and data assimilation for nonlinear differential equations
Jason Frank and Sergiy Zhuk · 2018
Cited alongside, same era.
Stochastic explosion and non-uniqueness for α \alpha -riccati equation
Radu Dascaliuc, Enrique A. Thomann, and Edward C. Waymire · 2018
Cited alongside, same era.
Hamiltonian simulation by qubitization
Guang Hao Low and Isaac L Chuang · 2019
Cited alongside, same era.
Product decomposition of periodic functions in quantum signal processing
Jeongwan Haah · 2019
Cited alongside, same era.
Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation
Xiang IA Yang and Kevin P Griffin · 2021
Cited alongside, same era.
Efficient quantum algorithm for dissipative nonlinear differential equations
Jin-Peng Liu, Herman Øie Kolden, Hari K Krovi, Nuno F Loureiro, Konstantina Trivisa, and Andrew M Childs · 2021
Cited alongside, same era.
Improved quantum algorithms for linear and nonlinear differential equations
Hari Krovi · 2023
Later among the works it cites.
Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
Dong An, Jin-Peng Liu, and Lin Lin · 2023
Later among the works it cites.
Detectability and global observer design for 2d Navier–Stokes equations with uncertain inputs
Sergiy Zhuk, Mykhaylo Zayats, and Emilia Fridman · 2023
Later among the works it cites.
Reducing data resolution for better superresolution: Reconstructing turbulent flows from noisy observation
Kyongmin Yeo, Małgorzata J Zimoń, Mykhaylo Zayats, and Sergiy Zhuk · 2024
Later among the works it cites.
A polynomial-time classical algorithm for noisy quantum circuits
Thomas Schuster, Chao Yin, Xun Gao, and Norman Y Yao · 2024
Later among the works it cites.
Toward optimal circuit size for sparse quantum state preparation
Rui Mao, Guojing Tian, and Xiaoming Sun · 2024
Later among the works it cites.
Quantum algorithm for the advection-diffusion equation and the Koopman-von Neumann approach to nonlinear dynamical systems
Ivan Novikau and Ilon Joseph · 2025
Closest in time.
Quantum and classical algorithms for nonlinear unitary dynamics
Noah Brustle and Nathan Wiebe · 2025
Closest in time.
Quantum carleman linearization efficiency in nonlinear fluid dynamics
Javier Gonzalez-Conde, Dylan Lewis, Sachin S. Bharadwaj, and Mikel Sanz · 2025
Closest in time.
Simulating quantum circuit expectation values by Clifford perturbation theory
Tomislav Begušić, Kasra Hejazi, and Garnet Kin Chan · 2025
Closest in time.