This chapter explored many concepts. It is really an extension of Chapter 3 and the application of some of the elements of Chapter 1. This is likely to be one of the more difficult chapters for many readers, and it is strongly suggested that you read it more than once. While many topics were explored, some are absolutely critical for your understanding of quantum computing. The bra-ket notation is used throughout quantum computing, so ensure you are quite comfortable with it. Hamiltonians also play a prominent role in quantum computing. Quantum decoherence is actually a substantial impediment to the progress of quantum computing. To fully understand decoherence, you need to understand the wave function and associated equations. Quantum electrodynamics and quantum chromodynamics were presented to help round out your basic introduction to quantum theory. However, those two topics are a bit less critical for you to move forward with quantum computing.