Qubit in Quantum Computing
In quantum computing systems as in classical systems, two distinguishable states of the system are needed to represent a single bit of data. For example, consider the electron in a hydrogen atom. It can be in its ground state or an excited state as depicted in the figure:
If this were a classical system, it could be assumed as shown in the figure. The excited state represents a |1> and the ground state represents a |0>. In general, the electron is a quantum system, it may exist in a linear superposition of the ground and excited state. It is in the ground state(0) with probability amplitude α and the excited state(1) with probability amplitude β. Such a two-state quantum system is referred to as a qubit and its actual state Ψ can also be any linear combination of these basic states.
The state space of a qubit can be visualized by using an imaginary sphere that is known as the block sphere. It has a unit radius. The arrow on the sphere represents the state of the qubit. Its north and south poles are selected to represent the basis states |1> and |1>. While the state of a classical bit can be either the north or the south pole of the equator, a qubit can be any point on the sphere.
The Bloch sphere allows the state of a qubit to be represented using unit spherical coordinates, for example, the polar angle θ and the azimuth angle Φ. The Bloch sphere representation of a qubit is –
| Ψ >=cos (θ/2) |0> + e<sup>iΦ</sup> sin (θ/2) |1> Where 0 ≤ θ < π and 0 ≤ Φ < 2π.