Math for Qubits and Quantum Gates

In the previous chapter, we examined the idea of a qubit with its elusive behavior and its probabilistic nature. That chapter mentioned states other than |0⟩, |1⟩, and a halfway state but doesn’t describe any details about such states.

To understand the full range of states a qubit can have, we need some math, and this chapter lays the mathematical groundwork. We’ll start this chapter by replacing the intuitive halfway terminology with numbers. We’ll show how those numbers apply to a qubit’s state. We will send qubits through quantum computer circuits and compute the outcome using matrices.

Using our tools to represent circuits with matrices, we will discover the kinds of operations that a circuit can perform. We’ll combine these operations using matrix arithmetic. To bring these concepts into crystal clear focus, we’ll write code to run on a quantum computer.

We’ll cover the following...