Chapter 7
Small Step for Man—Single Qubit Programs

In the previous chapter, Chapter 6, ​Designer Genes—Custom Quantum States​, you saw how to precisely specify any quantum states. In this chapter, you’ll learn ways to manipulate qubits to any arbitrary quantum state.

The quantum programs you’ve seen so far have been somewhat limited. You’ve learned to invoke quantum phenomena in programs, got them to work predictably, and used the Qubelets Model, to analyze them. But to hook up more gates and deal with more qubits to solve big problems, you need to learn techniques that’ll let you handle larger circuits. In particular, because we need to consider the all-states-at-once nature of quantum computing, the bookkeeping gets more intricate. You’ll ratchet up your toolkit with techniques that show you how to keep track of the quantum states of qubits through a program’s circuitry without going through the one-bit-at-a-time way of individually tracing the qubelets in each qubit and tabulating where they end up.

In this chapter, you’ll work with single-qubit programs. Although single-qubit programs aren’t terribly exciting from an applications standpoint, the ideas and techniques you’ll learn here extend directly to multi-qubit programs in the next chapter. Moreover, the techniques described here will help you figure out which gates to use and how to connect them in your quantum circuit so that the mega-qubit and its quantum states end up where you want them to. This will help you design quantum algorithms for your own applications.