Fig. 4: Error analysis.

Here we plot the average fidelity as a function of (a) simulation time t, (b) frequency ω and (c) system size n. Unless varied, the parameters equal those of our hardware implementation in Fig. 3; namely J = 1, κ = 0.25, h = 2, ω = 30 and t = 22.75 T. Overall, we find an excellent agreement between our analytical error estimate (black) and the exact numerical calculations (cyan). (Note, we plot here the full 1st-order expression for the error given in Eq. (10) as derived in Supplementary Note IV.B). The yellow line indicates the exact error when \({\hat{H}}_{{\rm{eff}}}\) is expanded to second order in ω and the kick operator is expanded to first order in ω. (d)–(f) show the numerically calculated overhead of standard Trotterization R in terms of simulation time t, frequency ω and system size n. For first order QHiFFS (cyan) we observe linear, quadratic (since t is chosen in units of \(T=\frac{2\pi }{\omega }\)) and constant scalings with t, ω and n respectively (shown in red) as predicted by Eq. (11).