  Quantum state transfer (QST) describes the coherent passage of quantum
information from one node in a network to another. Experiments on QST span a
diverse set of platforms and currently report transport across up to tens of
nodes in times of several hundred nanoseconds with fidelities that can approach
90% or more. Theoretical studies examine both the lossless time evolution
associated with a given (Hermitian) lattice Hamiltonian and methods based on
the master equation that allows for losses. In this paper, we describe Monte
Carlo techniques which enable the discovery of a Hamiltonian that gives
high-fidelity QST. We benchmark our approach in geometries appropriate to
coupled optical cavity-emitter arrays and discuss connections to condensed
matter Hamiltonians of localized orbitals coupled to conduction bands. The
resulting Jaynes-Cummings-Hubbard and periodic Anderson models can, in
principle, be engineered in appropriate hardware to give efficient QST.
