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Suppressing the Trotter error in dynamical quantum simulation typically requires running deeper circuits, posing a great challenge for noisy near-term quantum devices.
1907
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N. Hatano and M. Suzuki, Finding exponential product formulas of higher orders, in Quantum Annealing and Other Optimization Methods , edited by A. Das and B. K. Chakrabarti (Springer Berlin Heidelberg, Berlin, Heidelberg, 2005) pp. 37–68
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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
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A. M. Childs, A. Ostrander, and Y. Su, Faster quantum simulation by randomization, Quantum 3
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A. M. Childs and Y. Su, Nearly optimal lattice simulation by product formulas, Phys. Rev. Lett. 123
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I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, H. Neven, and R. Babbush, Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization, Quantum 4
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A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu, Theory of trotter error with commutator scaling, Phys. Rev. X 11
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M. Heyl, P. Hauke, and P. Zoller, Quantum localization bounds trotter errors in digital quantum simulation, Science Advances 5
2019
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M. C. Tran, S.-K. Chu, Y. Su, A. M. Childs, and A. V. Gorshkov, Destructive error interference in product-formula lattice simulation, Phys. Rev. Lett. 124
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Observe that this is a geometric series applied to the operator ad H \text{ad}_{H} , which is a diagonal matrix in H H ’s eigen-operator representation | i ⟩ ⟨ j | |i\rangle\langle j| (Appendix B
Cited in the paper.
Setting the right-hand side of Eq. ( 13
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To clarify, the value of the O ( τ 2 ) O(\tau^{2}) term is a complicated combination of many oscillations and it could look linear in a particular period under certain circumstances, but we call it constant-in-t in the sense that its overall effect is oscillation that does not grow with time asymptotically
Cited in the paper.
The analysis holds well for r ‖ δ ‖ ≪ 1 r||\delta||\ll 1 . Since r ‖ δ ‖ = O ( τ 2 t ) r||\delta||=O(\tau^{2}t) for second-order PF, under a fixed step size τ = t / r \tau=t/r , it implies t ≪ 1 τ 2 t\ll\frac{1}{\tau^{2}}
Cited in the paper.
Later among the works it cites.
J. Haah, M. B. Hastings, R. Kothari, and G. H. Low, Quantum algorithm for simulating real time evolution of lattice hamiltonians, SIAM Journal on Computing 52
2023
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W. W. Ho, T. Mori, D. A. Abanin, and E. G. Dalla Torre, Quantum and classical floquet prethermalization, Annals of Physics 454
2023
Later among the works it cites.