A qubit, which is the fundamental unit of information in quantum computing, can exist in a superposition of two states. These two states are typically denoted as |0⟩ and |1⟩, representing the basis states of the qubit. Each state corresponds to a distinct quantum state and can be thought of as analogous to the classical binary states of 0 and 1.
The key characteristic of a qubit is its ability to exist in a coherent superposition of these basis states. This means that a qubit can be in a combination of |0⟩ and |1⟩ simultaneously. Mathematically, the qubit state can be represented as α|0⟩ + β|1⟩, where α and β are complex probability amplitudes that determine the probability of observing the qubit in the |0⟩ and |1⟩ states, respectively.
In this superposition, the amplitudes α and β must satisfy normalization conditions, such that the sum of their squared magnitudes equals 1: |α|^2 + |β|^2 = 1. This constraint ensures that when a measurement is made on the qubit, the probability of observing either |0⟩ or |1⟩ is well-defined and adds up to 100%.
Therefore, while a qubit can exist in a superposition of two basis states, it ultimately collapses into one of those states upon measurement, with the probability of each outcome determined by the amplitudes α and β. This unique property of qubits enables quantum computers to perform certain types of computations in parallel and exhibit quantum phenomena such as entanglement and quantum interference.