3 Single-qubit states and gates

 

This chapter covers

  • Single-qubit quantum states and introducing state tables
  • Basic single-qubit quantum gates and single-qubit quantum circuits
  • Simulating single-qubit quantum systems in Python

In this chapter, we look at the state of a single-qubit system with programmatic and visual representations. We also cover how a qubit can be used as a computational tool. In the next chapter, we will generalize these concepts to any number of qubits.

The simplest representation of a quantum state in code is a list of complex numbers. This list is often called a state vector. We will use state tables like the ones introduced in chapter 2 to visualize quantum states.

This chapter also introduces the basics of applying programming instructions, called quantum gates, to a single-qubit system and combining them into a quantum circuit. We will look at some ways to visualize gates and circuits. Finally, we will examine a few simple single-qubit circuits with practical applications. Figure 3.1 shows the structure of the concepts introduced in this chapter.

Figure 3.1 A dependency diagram of concepts introduced in this chapter
figure

Note  The source code, examples, and exercise answers can be found on the book’s website (www.manning.com/books/building-quantum-software-with-python) and in the book’s companion repository (https://github.com/learnqc/code).

3.1 Single-qubit state: A pair of complex numbers

3.1.1 Visualizing single-qubit states with tables

3.1.2 The general form of a single-qubit state

3.1.3 Programmatically encoding single-qubit states with lists

3.1.4 Implementing a single-qubit quantum computing simulator in Python

3.2 Changing amplitudes with single-qubit gates

3.2.1 Rotation is multiplication

3.2.2 Basic single-qubit gates

3.2.3 The general form of a single-qubit gate

3.2.4 More basic single-qubit gates

3.2.5 Single-qubit gate inverses

3.3 Simulating changing amplitudes with gates

3.3.1 Printing and visualizing the state

3.3.2 Transforming a single-qubit state

Summary