@article {tran_destructive_2020, title = {Destructive {Error} {Interference} in {Product}-{Formula} {Lattice} {Simulation}, journal = {Phys. Rev. Lett.}, volume = {124}, number = {22}, year = {2020}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, month = {jun}, abstract = {Quantum computers can efficiently simulate the dynamics of quantum systems. In this Letter, 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 + nt(3)/r(2)) when nt(2)/r is less than a small constant. Given an error tolerance epsilon, the error bound yields an estimate of max\{O(n(2)t/epsilon), O(n(2)t(3/2)/epsilon(1/2))\} 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. [Proc. Natl. Acad. Sci. U.S.A. 115, 9456 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.124.220502}, author = {Tran, Minh C. and Chu, Su-Kuan and Su, Yuan and Childs, Andrew M. and Gorshkov, V, Alexey} }