Two-Qubit Gates
Two-qubit gates are 4x4 unitaries that can entangle qubits; at least one entangling gate is required for universal quantum computation.
Why two qubits are special
A two-qubit gate is a 4x4 unitary acting on the joint space of two qubits. Unlike single-qubit gates, a two-qubit gate can create entanglement, which is why at least one is indispensable for universal computation.
Common examples
- CNOT: flips target if control is |1> (the standard entangler)
- CZ (controlled-Z): applies a phase of -1 to |11>
- SWAP: exchanges the two qubits' states
- iSWAP and sqrt(iSWAP): native to many superconducting platforms
Entangling versus non-entangling
Not every two-qubit gate entangles. SWAP, for instance, only relabels qubits and creates no entanglement from a product input. A gate is entangling if it can turn some product state into an entangled one; CNOT and CZ do, SWAP does not. Universality requires an entangling gate specifically.
Hardware-native gates
Each platform has a natural two-qubit interaction determined by its physics. Superconducting chips often implement CZ or iSWAP; trapped ions use the Molmer-Sorensen gate. Compilers translate abstract CNOTs into whatever the hardware provides, so the logical circuit and the physical pulses can differ substantially.
The cost of entangling gates
Two-qubit gates are typically slower and noisier than single-qubit gates, so they dominate the error budget of a circuit. Reported two-qubit fidelities lag single-qubit ones, and reducing two-qubit gate count is a central goal of circuit optimisation. The threshold for error correction is set largely by two-qubit gate quality.