Introduction to Qubits

What is a Qubit?

A qubit (quantum bit) is the fundamental unit of quantum information, akin to a classical bit but with unique properties.

Can exist in a state of 0, 1, or both simultaneously (due to superposition).
Exhibits entanglement with other qubits, allowing for complex correlations.

Superposition

Superposition is a key principle in quantum mechanics where a qubit can be in multiple states at once.

Mathematically, a qubit state |ψ⟩ can be represented as:


|ψ⟩ = α|0⟩ + β|1⟩

where α and β are complex numbers satisfying the normalization condition |α|² + |β|² = 1.

Note: α and β represent the probability amplitudes of measuring the qubit in state |0⟩ or |1⟩, respectively.

Entanglement

Entanglement is a phenomenon where the states of two or more qubits become correlated.

For example, two entangled qubits can be represented as:


|Φ⟩ = (1/√2)(|00⟩ + |11⟩)

This means that measuring one qubit immediately determines the state of the other, regardless of the distance between them.

Measuring Qubits

When a qubit is measured, it collapses from its superposition state to one of the basis states.

The probabilities of measuring each state are given by the squares of the probability amplitudes:


P(0) = |α|², P(1) = |β|²

Important: Measurement disrupts the superposition, forcing the qubit to adopt a definite state.

Flowchart: Qubit State Measurement


graph TD;
    A[Start] --> B{Is Qubit in Superposition?};
    B -- Yes --> C[Measure Qubit];
    B -- No --> D[Return Current State];
    C --> E[Collapse to |0⟩ or |1⟩];
    E --> F[End];
    D --> F;

FAQ

What is the difference between a classical bit and a qubit?

A classical bit can be either 0 or 1, while a qubit can be in a state of 0, 1, or both simultaneously due to superposition.

Can qubits be physically realized?

Yes, qubits can be implemented using various physical systems, including photons, trapped ions, and superconducting circuits.

How do qubits interact in a quantum computer?

Qubits interact through quantum gates that manipulate their states, enabling complex computations.