Quantum Computing
Basic

Normalisation Constraint

The squared amplitudes of a qubit must sum to 1, ensuring total probability is 100 %.

Formula

∣α∣2+∣β∣2=1|\alpha|^2 + |\beta|^2 = 1

Variables

\alphaAmplitude of |0⟩
\betaAmplitude of |1⟩

Example

α = √(0.3), β = √(0.7) → 0.3 + 0.7 = 1 ✓

Did You Know?

This constraint is why qubits live on the surface of a sphere (the Bloch sphere) rather than inside it.

quantumnormalisationprobability

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More in Quantum Computing

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Qubit Superposition State

Intermediate

General state of a single qubit as a superposition of the computational basis states.

Hadamard Gate

Intermediate

Puts a qubit into an equal superposition — the most common single-qubit gate.

Pauli-X Gate (Quantum NOT)

Basic

Flips |0⟩ to |1⟩ and vice versa — the quantum equivalent of a classical NOT gate.

CNOT Gate

Intermediate

Two-qubit gate that flips the target qubit only when the control qubit is |1⟩.

Bell State (EPR Pair)

Intermediate

Maximally entangled two-qubit state — measuring one qubit instantly determines the other.

Born Rule (Measurement Probability)

Intermediate

Probability of measuring outcome |k⟩ from a quantum state |ψ⟩.