6.9 Summary
In this chapter, we covered the elements of probability necessary for our treatment of quantum computing and its applications. When we work with qubits and circuits in the following chapters, we will use discrete sample spaces, although they can get quite large. In these cases, the sizes of the sample spaces will be powers of 2.
Our goal in a quantum algorithm is to adjust the probability distribution so that the element in the sample space with the highest probability is the best solution to some problem. Indeed, the manipulation of probability amplitudes leads us to find what we hope is the best answer. My treatment of algorithms in Chapter 9, “Wiring Up the Circuits,” and Chapter 10, “From Circuits to Algorithms,” does not go deeply into probability calculations, but it does so sufficiently to give you an idea of how probability interacts with interference, complexity, and the number of times we must run a calculation to be confident...
