Here C n,ν is the coupling of n th exciton to the ν th bath mode coordinate (R n,ν ) within the i th trajectory. Using Eq. 39 and Eq. 40 we can convert the simple hadamard product in Eq. 28 of Paper I (Ref. 1) as a collective Hadamard product of "m" trajectories through the Hadamard product between the batch matrices, {ϵ} m ⊙ {|Ψ⟩} m .