Quantum Computing
Intermediate

Hadamard Gate

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

Formula

H=12(111−1)H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}

Variables

HHadamard gate matrix

Example

H|0⟩ = (|0⟩ + |1⟩)/√2

Did You Know?

Almost every quantum algorithm begins with Hadamard gates to create the superposition needed for quantum parallelism.

quantumhadamardgatesuperposition

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Qubit Superposition State

Intermediate

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

Normalisation Constraint

Basic

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

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⟩.