Basic Concepts of Qubits
Artyom M. Grigoryan, Sos S. Agaian · 2025
This chapter describes the basic concept and operations, called gates, on qubits. It explains the mathematical model of the qubit. The chapter presents the vision of a multiplicative qubit group using qubit multiplication and division operations. One can even solve quadratic equations with qubits. In the theory of quantum computation, a quantum bit, which is called a qubit, may be in two states, 0 and 1. Mathematically, a single qubit is defined as a linear combination of these basis states with given amplitudes a 0 and a 1 . Any quantum system with only two states can be considered as a qubit. A qubit can only be measured once, and only one of its states will be the result of the measurement. The chapter provides a list of single qubit gates and their description. It illustrates two circuits for preparation of the single qubit without and with a global phase.