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We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing.
E. P. Gross, “Structure of a quantized vortex in boson systems,” Il Nuovo Cimento 20
1961
Earlier work this paper cites.
L. P. Pitaevskii, “Vortex lines in an imperfect Bose gas,” JETP 13
1961
Earlier work this paper cites.
L. M. Milne-Thomson, Theoretical Aerodynamics (Dover Publications, New York, USA, 1973)
1973
Earlier work this paper cites.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, New York, USA, 1992)
1992
Earlier work this paper cites.
J. M. Spall, “Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation,” IEE Trans. Automat. Contr. 37
1992
Earlier work this paper cites.
B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys. 56
1993
Earlier work this paper cites.
M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73
1994
Earlier work this paper cites.
A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52
1995
Earlier work this paper cites.
S. Lloyd, “Universal Quantum Simulators,” Science 273
1996
Earlier work this paper cites.
A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, “Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions,” Rev. Mod. Phys. 68
1996
Earlier work this paper cites.
A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys. 73
2001
Earlier work this paper cites.
J. H. Ferziger and M. Perić, Computational Methods for Fluid Dynamics (Springer, Berlin, Germany, 2002)
2002
Earlier work this paper cites.
A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct Estimations of Linear and Nonlinear Functionals of a Quantum State,” Phys. Rev. Lett. 88
2002
Earlier work this paper cites.
S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer, New York, USA, 2003)
2003
Earlier work this paper cites.
L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, UK, 2003)
2003
Earlier work this paper cites.
C. M. Alves, P. Horodecki, D. K. L. Oi, L. C. Kwek, and A. K. Ekert, “Direct estimation of functionals of density operators by local operations and classical communication,” Phys. Rev. A 68
2003
Earlier work this paper cites.
G. Vidal, “Efficient Classical Simulation of Slightly Entangled Quantum Computations,” Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
A. J. Daley, C. Kollath, U. Schollwöck, and G. Vidal, “Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces,” J. Stat. Mech. 4
2004
Earlier work this paper cites.
A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, “Simulated Quantum Computation of Molecular Energies,” Science 309
2005
Earlier work this paper cites.
A. Scott, Encyclopedia of Nonlinear Science (Routledge, New York, USA, 2005)
2005
Earlier work this paper cites.
C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, “Sequential Generation of Entangled Multiqubit States,” Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
P. Lynch, The Emergence of Numerical Weather Prediction (Cambridge University Press, Cambridge, UK, 2006)
2006
Earlier work this paper cites.
G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, “Electronic structure calculations with dynamical mean-field theory,” Rev. Mod. Phys. 78
2006
Earlier work this paper cites.
V. V. Shende, S. S. Bullock, and I. L. Markov, “Synthesis of quantum-logic circuits,” IEEE Trans. on Computer-Aided Design 25
2006
Earlier work this paper cites.
H. K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics (Pearson Education Limited, Harlow, UK, 2007)
2007
Cited alongside, same era.
C. Grossmann, H.-G. Roos, and M. Stynes, Numerical Treatment of Partial Differential Equations (Springer, Berlin, Germany, 2007)
2007
Cited alongside, same era.
C. Schön, K. Hammerer, M. M. Wolf, J. I. Cirac, and E. Solano, “Sequential generation of matrix-product states in cavity QED,” Phys. Rev. A 75
2007
Cited alongside, same era.
I. Kassal, S. P. Jordan, P. J. Love, M. Mohseni, and A. Aspuru-Guzik, “Polynomial-time quantum algorithm for the simulation of chemical dynamics,” Proc. Natl. Acad. Sci. 105
2008
Cited alongside, same era.
F. Verstraete, V. Murg, and J. I. Cirac, “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems,” Adv. Phys. 57
R. Orús, “A practical introduction to tensor networks: Matrix product states and projected entangled pair states,” Ann. Phys. 349
2014
Later among the works it cites.
S. H. Strogatz, Nonlinear Dynamics and Chaos (Westview Press, Boulder, USA, 2015)
2015
Later among the works it cites.
D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, “Simulating Hamiltonian Dynamics with a Truncated Taylor Series,” Phys. Rev. Lett. 114
2015
Later among the works it cites.
A. Montanaro and S. Pallister, “Quantum algorithms and the finite element method,” Phys. Rev. A 93
2016
Later among the works it cites.
J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,” New Journal of Physics 18
2016
Later among the works it cites.
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2008
Cited alongside, same era.
M. C. Bañuls, D. Pérez-García, M. M. Wolf, F. Verstraete, and J. I. Cirac, “Sequentially generated states for the study of two-dimensional systems,” Phys. Rev. A 77
2008
Cited alongside, same era.
L. A. Aguirre and C. Letellier, “Modeling Nonlinear Dynamics and Chaos: A Review,” Mathematical Problems in Engineering 2009
2009
Cited alongside, same era.
A. W. Harrow, A. Hassidim, and S. Lloyd, “Quantum Algorithm for Linear Systems of Equations,” Phys. Rev. Lett. 103
2009
Cited alongside, same era.
I. Griva, S. G. Nash, and A. Sofer, Linear and Nonlinear Optimization (SIAM, Philadelphia, USA, 2009)
2009
Cited alongside, same era.
A. Iserles, A First Course in the Numerical Analysis of Differential Equations (Cambridge University Press, Cambridge, UK, 2009)
2009
Cited alongside, same era.
I. V. Oseledets, “Approximation of 2 d × 2 d 2^{d}\times 2^{d} Matrices Using Tensor Decomposition,” SIAM J. Matrix Anal. Appl. 31
2010
Cited alongside, same era.
B. Deissler, M. Zaccanti, G. Roati, C. D’Errico, M. Fattori, M. Modugno, G. Modugno, and M. Inguscio, “Delocalization of a disordered bosonic system by repulsive interactions,” Nature Phys. 6
2010
Cited alongside, same era.
P. J. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, R. Barends J. R. McClean, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley, C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, P. V. Coveney, P. J. Love, H. Neven, A. Aspuru-Guzik, and J. M. Martinis, “Scalable Quantum Simulation of Molecular Energies,” Phys. Rev. X 6
2016
Later among the works it cites.
R. Iten, R. Colbeck, I. Kukuljan, J. Home, and M. Christandl, “Quantum circuits for isometries,” Phys. Rev. A 93
2016
Later among the works it cites.
I. D. Kivlichan, N. Wiebe, R. Babbush, and A. Aspuru-Guzik, “Bounding the costs of quantum simulation of many-body physics in real space,” J. Phys. A: Math. Theor. 50
2017
Later among the works it cites.
A. M. Childs, R. Kothari, and R. D. Somma, “Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision,” SIAM J. Comput. 46
2017
Later among the works it cites.
Y. Li and S. C. Benjamin, “Efficient Variational Quantum Simulator Incorporating Active Error Minimization,” Phys. Rev. X 7
2017
Later among the works it cites.
A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
2017
Later among the works it cites.
J. I. Colless, V. V. Ramasesh, D. Dahlen, M. S. Blok, M. E. Kimchi-Schwartz, J. R. McClean, J. Carter, W. A. de Jong, and I. Siddiqi, “Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm,” Phys. Rev. X 8
2018
Later among the works it cites.
E. F. Dumitrescu, A. J. McCaskey, G. Hagen, G. R. Jansen, T. D. Morris, T. Papenbrock, R. C. Pooser, D. J. Dean, and P. Lougovski, “Cloud Quantum Computing of an Atomic Nucleus,” Phys. Rev. Lett. 120
2018
Later among the works it cites.
C. Hempel, C. Maier, J. Romero, J. McClean, T. Monz, H. Shen, P. Jurcevic, B. P. Lanyon, P. Love, R. Babbush, A. Aspuru-Guzik, R. Blatt, and C. F. Roos, “Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator,” Phys. Rev. X 8
2018
Later among the works it cites.
J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. J. Love, and A. Aspuru-Guzik, “Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz,” Quantum Sci. Technol. 4
2018
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
M. Lubasch, P. Moinier, and D. Jaksch, “Multigrid renormalization,” J. Comp. Phys. 372
2018
Later among the works it cites.
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2019
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A. W. Cross, L. S. Bishop, S. Sheldon, P. D. Nation, and J. M. Gambetta, “Validating quantum computers using randomized model circuits,” Phys. Rev. A 100
2019
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