The key distinction between classical bits and quantum bits (qubits) lies in their underlying principles and the way they represent and process information.
In classical computing, a bit can exist in one of two definite states: 0 or 1. When a classical bit is measured, it will always be observed as either a 0 or a 1, corresponding to one of those two states. This is known as deterministic behavior.
On the other hand, qubits in quantum computing can exist in a superposition of states. This means that a qubit can simultaneously be in a combination of both 0 and 1 states, with varying probabilities assigned to each state. Mathematically, we can represent a qubit as α|0⟩ + β|1⟩, where α and β are complex numbers called probability amplitudes and |0⟩ and |1⟩ are the basis states representing 0 and 1, respectively.
When a qubit is measured, however, it collapses into one of its basis states with a probability determined by the squared magnitudes of its probability amplitudes. For example, if α = 0.8 and β = 0.6, measuring the qubit will yield a 0 with a 64% probability (0.8^2) and a 1 with a 36% probability (0.6^2). The measurement outcome is probabilistic rather than deterministic.
The power of qubits comes from their ability to exist in these superposition states, allowing for parallel processing and the potential to perform certain computations more efficiently than classical systems. By manipulating and controlling qubits using quantum gates, quantum algorithms can exploit the interference and entanglement properties of qubits to solve specific problems with greater speed or efficiency.
So, while the measurement of a qubit ultimately yields a classical bit (either 0 or 1), the ability of qubits to exist in superposition states before measurement allows for a richer and more powerful representation and manipulation of information than classical bits can achieve.