%0 Journal Article %J Phys. Rev. Lett. %D 2020 %T Destructive Error Interference in Product-Formula Lattice Simulation %A Minh C. Tran %A Su-Kuan Chu %A Yuan Su %A Andrew M. Childs %A Alexey V. Gorshkov %X
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.
%B Phys. Rev. Lett. %V 124 %8 6/4/2020 %G eng %U https://arxiv.org/abs/1912.11047 %N 220502 %R https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502