In a quantum computer, a qubit can exist in three possible states, known as the computational basis states. These states are represented by vectors in a two-dimensional complex vector space.
State |0⟩: This state corresponds to the qubit being in the "0" state. It is typically represented as a vector [1, 0] or simply |0⟩. In this state, the qubit has a high probability of being measured as a classical bit in the state 0.
State |1⟩: This state corresponds to the qubit being in the "1" state. It is typically represented as a vector [0, 1] or simply |1⟩. In this state, the qubit has a high probability of being measured as a classical bit in the state 1.
Superposition states: Apart from the individual states |0⟩ and |1⟩, a qubit can exist in a superposition of these states. A superposition is a combination of the |0⟩ and |1⟩ states, and it is represented as a linear combination of these basis states. For example, a qubit can be in a state represented by (α|0⟩ + β|1⟩), where α and β are complex numbers that determine the probability amplitudes of the respective states. In a superposition state, the qubit simultaneously exists in both the |0⟩ and |1⟩ states with different probabilities, and it can be measured as either 0 or 1 with corresponding probabilities determined by the coefficients α and β.
These three states form the basis for the computation and information processing in a quantum computer. By manipulating and controlling the quantum states of qubits through quantum gates and operations, quantum algorithms can take advantage of the superposition and entanglement properties of qubits to perform computations that may outperform classical algorithms for specific tasks.