In quantum computing, the information is encoded in qubits. A qubit or quantum bit is the basic unit of information in quantum computing. It is the quantum mechanical analog of a classical bit. It is a two-level quantum system where the two basis qubit states are usually written as |0> and |1>. A qubit state can be in |0>,|1>, or in a linear combination of both states. This is called superposition, which we will go into a little more later.
The two orthogonal z-basis states of a qubit are defined as:
Here, we implicitly refer to the z-basis states as computational basis states. The basis states are located on opposite points on the Bloch Sphere representation of the state of a single qubit.
There are several physical implementations of qubits. One example is two of the discrete energy levels of an ion or the spin states of an electron.
Superposition gives quantum computers superior computing power in specific cases. This is because instead of two bits only representing one of the four possible states (00,01,10,11) at a time, two qubits can represent all four states simultaneously.
With superposition, some calculations it would take classical computers millions of years to solve qubits can perform in minutes. Superposition enables quantum algorithms to utilize other quantum mechanical phenomenon like entanglement. Multiple qubits exhibit quantum entanglement when they correlate with each other to form a single system.