g-sim: transfer-matrix coordinate propagation

With respect to a Hilbert–Schmidt-orthonormal Hermitian basis $\{B_j\}_{j=1}^{\dim\mathfrak g}$ of $i\mathfrak g$, write the coordinate vector $c(X)=\big(\langle B_j,X\rangle_{\mathrm{HS}}\big)_{j=1}^{\dim\mathfrak g}$. For a circuit $U=\prod_{k=1}^{L}e^{i A_k}$ with generators in $\mathfrak g$, the coordinates of the Heisenberg-evolved observable follow from those of $O$ by an ordered product of per-gate $\dim\mathfrak g\times\dim\mathfrak g$ transfer matrices, $$c\big(\mathcal H(O)\big)=G_L\cdots G_1\,c(O),\qquad (G_k)_{ij}=\big\langle B_i,\,e^{-i A_k}B_j\,e^{i A_k}\big\rangle_{\mathrm{HS}}=\big(e^{-i\,\operatorname{ad}_{A_k}}\big)_{ij},$$ where $\operatorname{ad}_{A_k}(X)=[A_k,X]$. Each $G_k$ is the adjoint action of one gate written in the basis, so the entire g-sim update runs in the $\dim\mathfrak g$-dimensional coordinate space.