Tuning coupled cavity arrays Hamiltonians with Monte-Carlo methods*

We used Monte-Carlo techniques to tune coupled cavity array hopping parameters for perfect quantum state transfer (QST). For coupled cavity arrays with single excitations, we were able to find multiple cavity-emitter topologies which exhibited perfect QST. This is unique, as most existing work is cavity only. We developed two methods to tune the array hopping parameters. One set the Hamiltonian eigenvalues to a list of known eigenvalues, while the second set the time evolution operator to a predetermined matrix. The second method is of considerable interest, as it is easily generalized to multiple excitations. We will also show that using these methods, it is possible to "program" a coupled cavity array for a quite general time dependent behavior.