Quantum Computing

Intermediate

CNOT Gate

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

Formula

CNOT = \begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&0&1 \\ 0&0&1&0 \end{pmatrix}

Variables

CNOTControlled-NOT matrix

Example

CNOT|10⟩ = |11⟩; CNOT|00⟩ = |00⟩

Did You Know?

The Hadamard + CNOT combo is the standard recipe for creating entangled Bell states.

quantum cnot entanglement gate

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More in Quantum Computing

Qubit Superposition State

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

Normalisation Constraint

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

Hadamard Gate

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

Pauli-X Gate (Quantum NOT)

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

Bell State (EPR Pair)

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

Born Rule (Measurement Probability)

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