Fetching the paper…
Reading the bibliography…
Product formula approximations of the time-evolution operator on quantum computers are of great interest due to their simplicity, and good scaling with system size by exploiting commutativity between Hamiltonian terms.
H. F. Trotter, “On the Product of Semi-Groups of Operators,” Proceedings of the American Mathematical Society 10
1959
Earlier work this paper cites.
M. Suzuki, “Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations,” Physics Letters A 146
1990
Earlier work this paper cites.
S. Lloyd, “Universal Quantum Simulators,” Science 273
1996
Earlier work this paper cites.
C. S. Lam, “Decomposition of time-ordered products and path-ordered exponentials,” Journal of Mathematical Physics 39
1998
Earlier work this paper cites.
S. Blanes, F. Casas, and J. Ros, “Improved High Order Integrators Based on the Magnus Expansion,” BIT Numerical Mathematics 40
2000
Earlier work this paper cites.
M. Rudelson and R. Vershynin, “Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements,” in 2006 40th Annual Conference on Information Sciences and Systems (IEEE, 2006) pp. 207–212
2006
Earlier work this paper cites.
D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, “Efficient Quantum Algorithms for Simulating Sparse Hamiltonians,” Communications in Mathematical Physics 270
2007
Earlier work this paper cites.
S. A. Chin, “Multi-product splitting and Runge-Kutta-Nyström integrators,” Celestial Mechanics and Dynamical Astronomy 106
2010
Earlier work this paper cites.
N. Wiebe, D. Berry, P. Høyer, and B. C. Sanders, “Higher order decompositions of ordered operator exponentials,” Journal of Physics A: Mathematical and Theoretical 43
2010
Earlier work this paper cites.
D. Poulin, A. Qarry, R. Somma, and F. Verstraete, “Quantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of Hilbert Space,” Physical Review Letters 106
2011
Cited alongside, same era.
S. P. Jordan, K. S. M. Lee, and J. Preskill, “Quantum Algorithms for Quantum Field Theories,” Science 336
2012
Cited alongside, same era.
A. M. Childs and N. Wiebe, “Hamiltonian Simulation Using Linear Combinations of Unitary Operations,” Quantum Information & Computation 12
2012
Cited alongside, same era.
D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, “Exponential improvement in precision for simulating sparse Hamiltonians,” in Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC ’14 , STOC ’14 (ACM Press, New York, New York, USA, 2014) pp. 283–292
2014
Cited alongside, same era.
J. Haah, M. Hastings, R. Kothari, and G. H. Low, “Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians,” in 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) , FOCS ’18 (IEEE, Washington, DC, USA, 2018) pp. 350–360
2018
Later among the works it cites.
2018
Later among the works it cites.
E. Campbell, “A random compiler for fast Hamiltonian simulation,” Physical Review Letters (Accepted)
2019
Closest in time.
G. H. Low, “Hamiltonian simulation with nearly optimal dependence on spectral norm,” in Proceedings of the 51st Annual ACM Symposium on Theory of Computing - STOC ’19 (ACM Press, New York, New York, USA, 2019) pp. 491–502
2019
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
D. W. Berry, A. M. Childs, and R. Kothari, “Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters,” in 2015 IEEE 56th Annual Symposium on Foundations of Computer Science , FOCS ’15 (IEEE, Washington, DC, USA, 2015) pp. 792–809
2015
Cited alongside, same era.
D. Poulin, M. B. Hastings, D. Wecker, N. Wiebe, A. C. Doherty, and M. Troyer, “The Trotter step size required for accurate quantum simulation of quantum chemistry,” Quantum Information & Computation 15
2015
Cited alongside, same era.
R. D. Somma, “A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation,” Journal of Mathematical Physics 57
2016
Cited alongside, same era.
M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, “Elucidating reaction mechanisms on quantum computers,” Proceedings of the National Academy of Sciences 114
2017
Cited alongside, same era.
A. M. Childs, D. Maslov, Y. Nam, N. J. Ross, and Y. Su, “Toward the first quantum simulation with quantum speedup,” Proceedings of the National Academy of Sciences 115
2018
Cited alongside, same era.
D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, “Simulating Hamiltonian Dynamics with a Truncated Taylor Series,” Physical Review Letters 114
Cited in the paper.
G. H. Low and I. L. Chuang, “Optimal Hamiltonian Simulation by Quantum Signal Processing,” Physical Review Letters 118
Cited in the paper.
Cited in the paper.
G. H. Low and I. L. Chuang, “Hamiltonian Simulation by Qubitization,” Quantum 3
2019
Closest in time.
2019
Closest in time.
M. C. Tran, A. Y. Guo, Y. Su, J. R. Garrison, Z. Eldredge, M. Foss-Feig, A. M. Childs, and A. V. Gorshkov, “Locality and Digital Quantum Simulation of Power-Law Interactions,” Physical Review X 9
2019
Closest in time.
A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, “Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,” in Proceedings of the 51st Annual ACM Symposium on Theory of Computing - STOC ’19 (ACM Press, New York, New York, USA, 2019) pp. 193–204
2019
Closest in time.