7
One Qubit

Anyone who is not shocked by
quantum theory has not understood it.

Niels Bohr [1]

A quantum bit, or qubit, is the fundamental information unit of quantum computing. In this chapter, I give a mathematical definition of a qubit based on the foundational material in the first part of this book. Together we examine the operations you can perform on a single qubit from both mathematical and computational perspectives.

Despite a single qubit living in a seemingly strange two-dimensional complex Hilbert space, we can visualize it, its superposition, and its behavior by projecting onto the surface of a sphere in R³.

All vector spaces considered in this chapter are over C, the field of complex numbers introduced in section 3.9

Topics covered in this chapter

7.1 Introducing quantum bits
7.2 Bras and kets
7.3 The complex math and physics of a single qubit
7.3.1 Quantum state representation...