Quantum Computing
Intermediate

Born Rule (Measurement Probability)

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

Formula

P(∣k⟩)=∣⟨k∣ψ⟩∣2P(|k\rangle) = |\langle k|\psi\rangle|^2

Variables

P(|k\rangle)Probability of outcome k
\langle k|\psi\rangleInner product (amplitude)

Example

|ψ⟩ = (√0.3)|0⟩ + (√0.7)|1⟩ → P(0) = 30 %, P(1) = 70 %

Did You Know?

Max Born won the 1954 Nobel Prize for this single insight — that quantum amplitudes give probabilities via their squared modulus.

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Qubit Superposition State

Intermediate

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

Normalisation Constraint

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

Hadamard Gate

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

Pauli-X Gate (Quantum NOT)

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

CNOT Gate

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

Bell State (EPR Pair)

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