Quantum bits, or qubits, are the fundamental units of information in quantum computing. Unlike classical bits, which can only exist in states of 0 or 1, qubits can exist in a superposition of states, representing a combination of 0 and 1 simultaneously.
The number of states a qubit can have is determined by its quantum mechanical properties. Mathematically, a qubit can be represented as a vector in a two-dimensional complex vector space. This vector can be expressed as a linear combination of two basis states, conventionally denoted as |0⟩ and |1⟩. These basis states represent the classical states of 0 and 1, respectively.
In quantum mechanics, any complex linear combination of two states is valid, as long as the vector has unit length. Therefore, a qubit can exist in any superposition of |0⟩ and |1⟩. This means that a qubit can have an infinite number of possible states, represented by complex numbers that describe the coefficients of the linear combination.
To summarize, a qubit can be in any superposition of the basis states |0⟩ and |1⟩, allowing for a continuous range of possible states. However, when it comes to measurement, a qubit will collapse into one of the two basis states with a probability determined by the coefficients in the superposition.