It is an open question what advantages a quantum neural network (QNN) would have over a classical network. It has been shown that QNNs should have roughly the same computational power as classical networks [7]. Other results have shown that QNNs may work best with some classical components as well as quantum components [2]. Quantum searches can be proven to be faster than comparable classical searches. We leverage this idea to propose a new training method for a simple QNN. This paper details such a network and how training could be done on it. Results from testing the algorithm on several real-world problems show that it works.