Qubits

In classical computing, a bit can be either 0 or 1. A qubit (quantum bit) is the quantum equivalent — but with superpowers!

A qubit can be in state |0⟩, state |1⟩, or a superposition of both simultaneously. This is written mathematically as:

|ψ⟩ = α|0⟩ + β|1⟩

where α and β are complex numbers called amplitudes, and |α|² + |β|² = 1.

Qubits can be physically realized using:

• Photon polarization — horizontal vs. vertical

• Electron spin — up vs. down

• Superconducting circuits — used by Google and IBM

• Trapped ions — individual atoms held by electric fields

Each approach has trade-offs in terms of coherence time, error rates, and scalability.

The state of a single qubit can be visualized on the Bloch sphere — a unit sphere where:

• |0⟩ is at the north pole

• |1⟩ is at the south pole

• Points on the equator represent equal superpositions with different phases

Any single-qubit state maps to a point on this sphere, described by angles θ (theta) and φ (phi):

|ψ⟩ = cos(θ/2)|0⟩ + e^(iφ) sin(θ/2)|1⟩

When we measure a qubit in the computational basis:

• We get |0⟩ with probability |α|²

• We get |1⟩ with probability |β|²

Key insight: Measurement is irreversible — it collapses the superposition! After measurement, the qubit is definitively in the measured state.

This is fundamentally different from classical computing, where reading a bit doesn't change its value.