Fetching the paper…
Reading the bibliography…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous.
“Quantum algorithm for systems of linear equations with exponentially improved dependence on precision”
Andrew. Childs, Robin Kothari and Rolando. Somma · 1950
Earlier work this paper cites.
“Stochastic liouville equations”
Ryogo Kubo · 1963
Earlier work this paper cites.
“Linear transport theory”
Kenneth. Case · 1967
Earlier work this paper cites.
“Quantum detection and estimation theory”
Carl. Helstrom · 1969
Earlier work this paper cites.
“A modified Korteweg de Vries equation for ion acoustic waves”
Kimiaki Konno and Yoshi H · 1974
Earlier work this paper cites.
“The heat equation”
David Widder · 1976
Earlier work this paper cites.
“Simulating physics with computers”
Richard. Feynman · 1982
Earlier work this paper cites.
“Soliton models of long internal waves”
Harvey Segur and J.. Hammack · 1982
Earlier work this paper cites.
“The one-dimensional heat equation”
John Cannon · 1984
Earlier work this paper cites.
“On measures of nonnormality of matrices”
L. Elsner and M.H.C. Paardekooper · 1987
Earlier work this paper cites.
“Elementary Bernoulli-Euler beam theory”
E.. Witmer · 1991
Earlier work this paper cites.
“Quantum theory: concepts and methods”
Asher Peres · 1995
Earlier work this paper cites.
“The quantum theory of fields”
Steven Weinberg · 1995
Earlier work this paper cites.
“Universal quantum simulators”
Seth Lloyd · 1996
Earlier work this paper cites.
“Transport equations for elastic and other waves in random media”
Leonid Ryzhik, George Papanicolaou and Joseph. Keller · 1996
Earlier work this paper cites.
“Nonlinear quantum mechanics implies polynomial-time solution for 𝑁𝑃 \mathit{NP} -complete and # P \mathit{P} problems”
Daniel. Abrams and Seth Lloyd · 1998
Earlier work this paper cites.
“Relativistic quantum mechanics and field theory”
Franz Gross · 1999
Earlier work this paper cites.
“Quantum state discrimination”
Anthony Chefles · 2000
Earlier work this paper cites.
“Relativistic quantum mechanics”
Walter Greiner · 2000
Earlier work this paper cites.
“Quantum computation and quantum information”
Michael. Nielsen and Isaac Chuang · 2000
Earlier work this paper cites.
“Creating superpositions that correspond to efficiently integrable probability distributions”, 2002
Lov Grover and Terry Rudolph · 2002
Earlier work this paper cites.
“Numerical solution of time-dependent advection-diffusion-reaction equations”
Willem. Hundsdorfer and Jan. Verwer · 2003
Earlier work this paper cites.
“Improved algorithms for approximate quantum Fourier transforms and sparse Hamiltonian simulations”
Graeme. Ahokas · 2004
Earlier work this paper cites.
“Quantum computing, postselection, and probabilistic polynomial-time”
Scott Aaronson · 2005
Earlier work this paper cites.
“Efficient quantum algorithms for simulating sparse Hamiltonians”
Dominic. Berry, Graeme Ahokas, Richard Cleve and Barry. Sanders · 2007
Earlier work this paper cites.
“A lower bound on the probability of error in quantum state discrimination”
Ashley Montanaro · 2008
Earlier work this paper cites.
“Methods of mathematical physics: partial differential equations”
Richard Courant and David Hilbert · 2008
Earlier work this paper cites.
“On the relationship between continuous- and discrete-time quantum walk”
Andrew. Childs · 2009
Earlier work this paper cites.
“Quantum algorithm for linear systems of equations”
Aram. Harrow, Avinatan Hassidim and Seth Lloyd · 2009
Earlier work this paper cites.
“Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer”
David Poulin and Pawel Wocjan · 2009
Earlier work this paper cites.
“Euler-Bernoulli beam theory”
Oliver. Bauchau and James. Craig · 2009
Cited alongside, same era.
“Numerical analysis”
Richard. Burden and J. Faires · 2010
Cited alongside, same era.
“Partial differential equations”
Lawrence. Evans · 2010
Cited alongside, same era.
“Random walk and the heat equation”
Gregory. Lawler · 2010
Cited alongside, same era.
“Quantum computing: A gentle introduction”
Eleanor. Rieffel and Wolfgang. Polak · 2011
Cited alongside, same era.
“The diffusion handbook: applied solutions for engineers”
R.. Thambynayagam · 2011
Cited alongside, same era.
“Beam structures: classical and advanced theories”
Erasmo Carrera, Gaetano Giunta and Marco Petrolo · 2011
“Nearly optimal lattice simulation by product formulas”
Andrew. Childs and Yuan Su · 2019
Later among the works it cites.
“The Power of Block-Encoded Matrix Powers: Improved Regression Techniques via Faster Hamiltonian Simulation”
Shantanav Chakraborty, András Gilyén and Stacey Jeffery · 2019
Later among the works it cites.
“Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing”
Yiğit Subaşı, Rolando. Somma and Davide Orsucci · 2019
Later among the works it cites.
“Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics”
András Gilyén, Yuan Su, Guang Low and Nathan Wiebe · 2019
Later among the works it cites.
“Quantum fast-forwarding: Markov chains and graph property testing”
Simon Apers and Alain Sarlette · 2019
Later among the works it cites.
“Quantum algorithm for simulating the wave equation”
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
“Black-box Hamiltonian simulation and unitary implementation”
Dominic. Berry and Andrew. Childs · 2012
Cited alongside, same era.
“Semiconductor equations”
Peter. Markowich, Christian. Ringhofer and Christian Schmeiser · 2012
Cited alongside, same era.
“Growth, reaction, movement and diffusion from biology”
Benoıt Perthame · 2012
Cited alongside, same era.
“Applied partial differential equations with Fourier series and boundary value problems”
Richard Haberman · 2012
Cited alongside, same era.
“Radiative transfer”
Subrahmanyan Chandrasekhar · 2013
Cited alongside, same era.
Pedro.. Costa, Stephen Jordan and Aaron Ostrander · 2019
Later among the works it cites.
“Quantum spectral methods for differential equations”
Andrew. Childs and Jin-Peng Liu · 2020
Later among the works it cites.
“Quantum simulation via randomized product formulas: low gate complexity with accuracy guarantees”, 2020
Chi-Fang Chen, Hsin-Yuan Huang, Richard Kueng and Joel. Tropp · 2020
Later among the works it cites.
“Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems”
Lin Lin and Yu Tong · 2020
Later among the works it cites.
“Quantum algorithm for matrix functions by Cauchy’s integral formula”
Souichi Takahira, Asuka Ohashi, Tomohiro Sogabe and Tsuyoshi. Usuda · 2020
Later among the works it cites.
“Quantum SDP-solvers: better upper and lower bounds”
Joran Van, András Gilyén, Sander Gribling and Ronald de Wolf · 2020
Later among the works it cites.
“Efficient quantum algorithm for dissipative nonlinear differential equations”
Jin-Peng Liu, HermanØie Kolden, Hari. Krovi, Nuno. Loureiro, Konstantina Trivisa and Andrew. Childs · 2021
Later among the works it cites.
“Theory of Trotter error with commutator scaling”
Andrew. Childs, Yuan Su, Minh. Tran, Nathan Wiebe and Shuchen Zhu · 2021
Later among the works it cites.
“Hamiltonian simulation in the low-energy subspace”
Burak Şahinoğlu and Rolando. Somma · 2021
Later among the works it cites.
“Complexity of quantum state verification in the quantum linear systems problem”
Rolando. Somma and Yiğit Subaşı · 2021
Later among the works it cites.
“Time-dependent unbounded Hamiltonian simulation with vector norm scaling”
Dong An, Di Fang and Lin Lin · 2021
Later among the works it cites.
“Fast-forwarding quantum evolution”
Shouzhen Gu, Rolando. Somma and Burak Şahinoğlu · 2021
Later among the works it cites.
“A unified framework of quantum walk search”
Simon Apers, András Gilyén and Stacey Jeffery · 2021
Later among the works it cites.
“Fast inversion, preconditioned quantum linear system solvers, fast Green’s-function computation, and fast evaluation of matrix functions”
Yu Tong, Dong An, Nathan Wiebe and Lin Lin · 2021
Later among the works it cites.
Davide Orsucci and Vedran Dunjko · 2021
Later among the works it cites.
“Improved quantum algorithms for linear and nonlinear differential equations”
Hari Krovi · 2022
Closest in time.
“Time-marching based quantum solvers for time-dependent linear differential equations”
Di Fang, Lin Lin and Yu Tong · 2022
Closest in time.
“Quantum Linear System Solver Based on Time-Optimal Adiabatic Quantum Computing and Quantum Approximate Optimization Algorithm”
Dong An and Lin Lin · 2022
Closest in time.
“Optimal scaling quantum linear-systems solver via discrete adiabatic theorem”
Pedro.S. Costa, Dong An, Yuval. Sanders, Yuan Su, Ryan Babbush and Dominic. Berry · 2022
Closest in time.
“Private communication”, 2022
Aram. Harrow and Robin Kothari · 2022
Closest in time.
“Quantum simulation of real-space dynamics”
Andrew. Childs, Jiaqi Leng, Tongyang Li, Jin-Peng Liu and Chenyi Zhang · 2022
Closest in time.
“Quadratic speedup for spatial search by continuous-time quantum walk”
Simon Apers, Shantanav Chakraborty, Leonardo Novo and Jérémie Roland · 2022
Closest in time.
“Time-dependent Hamiltonian simulation of highly oscillatory dynamics and superconvergence for Schrödinger Equation”
Dong An, Di Fang and Lin Lin · 2022
Closest in time.
“Basics of statistical physics”
Harald.. Muller-Kirsten · 2022
Closest in time.