Fig. 5: 2-qubit depth scaling as a function of the Heisenberg chain size.
From: Efficient and practical Hamiltonian simulation from time-dependent product formulas
2-qubit depth to achieve average infidelity \({{\mathbb{E}}}_{\{\left\vert x\right\rangle \}}[1-| \langle x| {U}_{{{\rm{exact}}}}^{{\dagger} }U| x\rangle {| }^{2}]\le 0.01\) for the different TDS algorithms for a 1 × L Heisenberg chain with field strength of J = 1/8 and evolution time T = L. Unlike Fig. 2, we use average fidelity to be able to simulate larger systems. Again, the required depths follow a power law of the form d = aLk whose parameters a and k we determine via a least-squares fit and use to extrapolate to up to L = 100. We report the fit parameters a and k, also for different values of α, in Supplementary Fig. 5. Error bars are ±1 step and the shaded regions are the one-sigma confidence intervals of the extrapolations.
