Programming Quantum Computers

Chapter 6. Amplitude Amplification

In the previous chapter we showed how to build conventional arithmetic and logical operations that utilize the power of superposition. But when using a QPU, being able to perform computations in superposition is useless if we don’t have something clever up our sleeves to make sure that we’re actually able to READ out a solution.

In this chapter we introduce the first quantum primitive allowing us to manipulate superpositions into a form that we can reliably READ. We’ve already noted that there are many such primitives, each suited to different kinds of problems. The first we will cover is amplitude amplification.¹

Hands-on: Converting Between Phase and Magnitude

Very simply, amplitude amplification is a tool that converts inaccessible phase differences inside a QPU register into READable magnitude differences (and vice versa). As a QPU tool, it’s simple, elegant, powerful, and very useful.

Tip

Given that amplitude amplification converts phase differences into magnitudes, you might think that magnitude amplification would be a better name. However, “amplitude amplification” is commonly used in the wider literature to refer to the kind of primitive we describe here.

For example, suppose we have a four-qubit QPU register containing one of the three quantum states (A, B, or C), shown in Figure 6-1, but we don’t know which one.

Figure 6-1. Each ...