2019/12/23 by Minh C. Tran, Su-Kuan Chu, Yuan Su +2 · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevlett.124.220502
published as Phys. Rev. Lett. 124, 220502 (2020) · 9 pages, 2 figures
arxiv created 2019/12/23 · arxiv updated 2020/06/05
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(n2 t3/2/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.