



@article {2514,
	title = {Destructive Error Interference in Product-Formula Lattice Simulation},
	journal = {Phys. Rev. Lett. },
	volume = {124},
	year = {2020},
	month = {6/4/2020},
	abstract = {<p>Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ε, the error bound yields an estimate of max{O(n2t/ε),O(n2t3/2/ε1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.\&nbsp;</p>},
	doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502},
	url = {https://arxiv.org/abs/1912.11047},
	author = {Minh C. Tran and Su-Kuan Chu and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov}
}
