I am trying to implement the Mixer of the Max-Independent Set from The Quantum Alternating Operator Ansatz from this paper (arXiv) in Chapter 4.2, page 15 to 17. For every verice $v$ in the Graph this operator $H_{CX,v}$ is definded. ($nbhd(v)$ are all the neighbors of v) \begin{align*} H_{CX,v} &= X_{v} H_{NOR(x_{nbhd(v)})} \\ &= 2^{-D_{v}}X_{v}\prod_{w \in nbhd(v)}(I + Z_{w})\\ \end{align*}
Then the operators for all vertices are summed up. Are there any rules how to sum up operators? $$H_{CX} = \sum_{i = 0}^{n-1}H_{CX,v_{i}}$$
After that the exponential of the Matrix is calculated. I have no clue how to do that. $$U_{sim-CX}(\beta) = e^{-i\beta H_{CX}}$$
Should I maybe do a Hamiltonian-simulation or are there other ways for doing this?
