Title | Destructive Error Interference in Product-Formula Lattice Simulation |

Publication Type | Journal Article |

Year of Publication | 2019 |

Authors | Tran, MC, Chu, S-K, Su, Y, Childs, AM, Gorshkov, AV |

Date Published | 12/23/2019 |

Abstract | 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. |

URL | https://arxiv.org/abs/1912.11047 |