qubitssuperposition

Qubits in superposition represent a fundamental concept in quantum computing that distinguishes it from classical computing. Classical bits can exist in one of two states, 0 or 1. A qubit, however, can exist in a superposition of both 0 and 1 simultaneously. This means a qubit can be in a state that is a combination of 0 and 1, with certain probabilities for each.

Mathematically, the state of a qubit can be represented as a linear combination of the basis states |0⟩ and |1⟩, often written as α|0⟩ + β|1⟩. Here, α and β are complex numbers called probability amplitudes, and the square of their magnitudes (|α|² and |β|²) represent the probabilities of measuring the qubit in the |0⟩ or |1⟩ state, respectively. The sum of these probabilities must always equal one (|α|² + |β|² = 1).

The ability of qubits to exist in superposition allows quantum computers to explore a vast number of possibilities concurrently. This is a key reason why quantum computers are expected to outperform classical computers for certain types of problems, such as factoring large numbers or simulating complex molecules. When a measurement is performed on a qubit in superposition, its state collapses into either |0⟩ or |1⟩, according to the probabilities determined by its amplitudes.