where δ E is the spectral radius (the energy difference between the highest and the lowest eigenenergy for ĤQ ). For z ≤ 1, one only needs to include the first few terms of the expansion. In the Chebyshev expansion approach, a large time step ∆t or a higher spectral radius δ E results in a higher z value which necessitates the requirement of more number of terms in the expansion, Eq. 32.