Chapter 8
Giant Leap for Mankind—Multi-Qubit Programs

If you step back and think about it, it’s actually quite remarkable that a matrix is all it takes to tell you how it transforms any of the infinite quantum states of a single qubit: regardless of the number of pentagon and triangle qubelets, or their relative rotations, the gate matrix correctly expresses how the gate affects the qubit.

In this chapter, you’ll learn to generalize the matrix concept for gates that handle multiple qubits. As with single-qubit gate matrices, once you know how to represent multi-qubit gates, you can then hook up any configuration of gates and reliably predict how the qubits will collapse. But, as I pointed out at the end of the previous chapter, matrices aren’t an end to themselves, especially when dealing with many qubits. So it’s imperative to think about them intuitively and how they form the basis for patterns that can be applied to circuits and programs that use several qubits.

We’ll start by generalizing the notion of idealized states when working with multiple qubits. Then we’ll look at the single-qubit gate matrices, but from the perspective of deducing how the gate modifies the qubelets rather than as signatures for a specific gate. This viewpoint lets us formulate matrices for multi-qubit gates. Finally, you’ll learn to apply these methods to introduce quantum effects customized for your application. You’ll design a teleporting circuit by breaking it up into smaller and more manageable parts, a paradigm that’ll guide you when developing your quantum programs.