Qubit

The quantum analog of a classical bit, and the basic unit of quantum information.

A qubit (quantum bit) is a two-level quantum system that serves as the basic unit of information in quantum computing. Unlike a classical bit, which is definitively 0 or 1, a qubit can exist in a superposition of both states simultaneously.

Mathematical Description

A qubit’s state is described as:

$$|\psi ⟩=\alpha |0⟩+\beta |1⟩$$

where:

• $|0⟩$ and $|1⟩$ are the computational basis states
• $\alpha$ and $\beta$ are complex amplitudes
• $|\alpha {|}^2+|\beta {|}^2=1$ (normalization condition)

When measured, the qubit collapses to $|0⟩$ with probability $|\alpha {|}^2$ or to $|1⟩$ with probability $|\beta {|}^2$.

Physical Implementations

Qubits can be realized in many physical systems:

Key Properties

1. Superposition: A qubit can be in a combination of $|0⟩$ and $|1⟩$
2. Measurement collapse: Observing a qubit forces it into a definite state
3. No-cloning: You cannot copy an unknown qubit state (see No-Cloning Theorem)
4. Entanglement: Qubits can become correlated with other qubits (see Entanglement)

Visualization

The Bloch sphere provides a geometric visualization of a qubit’s state. Any pure qubit state corresponds to a point on the surface of a unit sphere:

• $|0⟩$ is at the north pole
• $|1⟩$ is at the south pole
• Superposition states lie elsewhere on the sphere

Why It Matters

The qubit is the foundation of everything in quantum computing. Understanding qubits is essential for understanding:

• Quantum gates (operations on qubits)
• Quantum circuits (sequences of gates)
• Quantum algorithms (computational procedures)

See also: Superposition, Bloch Sphere, Quantum State, Logical Qubit, Physical Qubit