Quantum Superposition
This is the essence of the quantum state. The coefficients α and β encode probability amplitudes, with the rule |α|² + |β|² = 1. This equation defines superposition, the ability of a qubit to exist in multiple states simultaneously. When measured, the system "collapses" to |0⟩ or |1⟩, but until that moment, it carries information across both dimensions, a property exploited in quantum parallelism and machine learning.
Qubits as Quantum Superposition:
|ψ⟩ = a|0⟩ + b|1⟩
|a|² is the probability that the qubit is in state |0⟩.
|b|² is the probability that the qubit is in state |1⟩.
|a|² + |b|² = 1