Title | Destructive Error Interference in Product-Formula Lattice {Simulation |
Publication Type | Journal Article |
Year of Publication | 2020 |
Authors | M. C. Tran, S-K. Chu, Y. Su, A. M. Childs, and |
Journal | Phys. Rev. Lett. |
Volume | 124 |
Date Published | jun |
ISSN | 0031-9007 |
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. |
DOI | 10.1103/PhysRevLett.124.220502 |