  We introduce a novel transpiler for the placement and routing of quantum
circuits on arbitrary target hardware architectures. We use finite-horizon, and
optionally discounted, reward functions to heuristically find a suitable
placement and routing policy. We employ a finite lookahead to refine the reward
functions when breaking a tie between multiple policies. We benchmark our
transpiler against multiple alternative solutions and on various test sets of
quantum algorithms to demonstrate the benefits of our approach.
