



01561nas a2200169   4500008004100000245007300041210006900114260001300183490000800196520105300204100001901257700001701276700001301293700002301306700002501329856003701354       2020                        eng d00aDestructive Error Interference in Product-Formula Lattice Simulation0 aDestructive Error Interference in ProductFormula Lattice Simulat  c6/4/20200 v1243 a<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>1 aTran, Minh, C.1 aChu, Su-Kuan1 aSu, Yuan1 aChilds, Andrew, M.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/1912.11047