Papers › Destructive Error Interference in Product-Formula Lattice Simulation
Destructive Error Interference in Product-Formula Lattice Simulation
Minh C. Tran, Su-Kuan Chu, Yuan Su, Andrew M. Childs, Alexey V. Gorshkov
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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 t^(3/2)/ϵ^(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. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.
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