Multiqubit gates are quantum gates that act on two or more qubits simultaneously. They are the mechanism by which entanglement is created and destroyed in a quantum circuit — a single-qubit gate acting on one qubit at a time can never entangle two qubits that started in a product state.

A single-qubit gate is a $2 \times 2$ unitary matrix. A two-qubit gate is a $4 \times 4$ unitary, a three-qubit gate is $8 \times 8$, and in general an $n$-qubit gate is a $2^n \times 2^n$ unitary. The most important two-qubit gate is the CX gate.

Most multiqubit gates in common use are controlled gates. A controlled-$U$ gate applies a single-qubit unitary $U$ to a target qubit if and only if all control qubits are in state $\lvert 1\rangle$. The CX gate is controlled-$X$. The Toffoli gate is doubly-controlled-$X$ (two control qubits). Any single-qubit gate $U$ has a controlled version, written $CU$, which is a $4 \times 4$ unitary acting as identity on the $\lvert 0\rangle$ control subspace and as $U$ on the $\lvert 1\rangle$ control subspace.

Single-qubit gates together with the CX gate form a universal gate set: any $n$-qubit unitary can be approximated to arbitrary precision using only these. In fault-tolerant quantum computing, the discrete set $\{H, T, \text{CX}\}$ is typically used instead, where the Solovay-Kitaev theorem guarantees that any single-qubit unitary can be efficiently approximated to within $\epsilon$ using $O(\log^c(1/\epsilon))$ gates.

• CX gate (CNOT) — controlled-NOT (CX); the standard entangling gate
• CCX (Toffoli) gate — doubly-controlled-NOT (CCX); classically universal
• SWAP gate — exchanges the states of two qubits
• iSWAP gate — swap with imaginary phase; native on superconducting hardware