  Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as
dynamic CTQWs, are a recently introduced universal model of computation that
offers a new paradigm in which to envision quantum algorithms. In this work we
develop a mapping from dynamic CTQWs to the gate model of computation in the
form of an algorithm to convert arbitrary single edge walks and single self
loop walks, which are the fundamental building blocks of dynamic CTQWs, to
their circuit model counterparts. We use this mapping to introduce an arbitrary
quantum state preparation framework based on dynamic CTQWs. Our approach
utilizes global information about the target state, relates state preparation
to finding the optimal path in a graph, and leads to optimizations in the
reduction of controls that are not as obvious in other approaches.
Interestingly, classical optimization problems such as the minimal hitting set,
minimum spanning tree, and shortest Hamiltonian path problems arise in our
framework. We test our methods against uniformly controlled rotations methods,
used by Qiskit, and find ours requires fewer CX gates when the target state has
a polynomial number of non-zero amplitudes.
