  Continuous-time quantum walks are natural tools for spatial search, where one
searches for a marked vertex in a graph. Sometimes, the structure of the graph
causes the walker to get trapped, such that the probability of finding the
marked vertex is limited. We give an example with two linked cliques, proving
that the captive probability can be liberated by increasing the weights of the
links. This allows the search to succeed with probability 1 without increasing
the energy scaling of the algorithm. Further increasing the weights, however,
slows the runtime, so the optimal search requires weights that are neither too
weak nor too strong.
