Fig. 3: Excitation dynamics using Trotter 2 and THRIFT 2.
From: Efficient and practical Hamiltonian simulation from time-dependent product formulas
Simulation of the propagation of an excitation in a 29-site transverse-field Ising model chain at h = 2 and J = 1 (α = 0.5) with 15 Trotter 2/THRIFT 2 steps. The initial state chosen here is \(\left\vert \psi (0)\right\rangle=\left\vert \downarrow \cdots \downarrow -\downarrow \cdots \downarrow \right\rangle \), with \(\left\vert -\right\rangle=(\left\vert \uparrow \right\rangle -\left\vert \downarrow \right\rangle )\sqrt{(2)}\). Clearly, the simulation with Trotter 2 starts to deviate significantly from the exact dynamics starting from T > 5, while the simulation with THRIFT 2 remains accurate for much longer times.
