Fig. 3: Setup of information propagation.
From: Effective light cone and digital quantum simulation of interacting bosons
We consider an operator \({O}_{{X}_{0}}\) supported on the subset X0 and approximate the time-evolved operator \({O}_{{X}_{0}}(t)\) onto the extended region X0[R] (enclosed by the orange shaded line). Additionally, we assume that the boson number distribution at each site is sub-exponentially suppressed for an initial state, as in Eq. (3). Then, as long as \(R\ge {t}^{D}{{{{{{{\rm{polylog}}}}}}}}(t)\), the approximation error between \({O}_{{X}_{0}}(t)\) by \(O({H}_{{X}_{0}[R]},t)\) decays sub-exponentially with R. The effective light cone for the information propagation grows polynomially with time as R ≈ t D.
