The Controlled-Phase (CZ) Gate
The CZ gate adds a phase only when both qubits are 1; on tunable superconducting qubits it is made by briefly using a higher energy level.
What CZ does
The controlled-Z gate leaves every computational-basis state unchanged except |11>, which acquires a minus sign. It is symmetric between the two qubits and is locally equivalent to CNOT (conjugate the target with Hadamards). Because it is diagonal, it composes cleanly with Z rotations and is a natural native gate on several platforms.
CZ (diagonal entries on basis 00,01,10,11)
The higher-level trick on transmons
On tunable transmons, CZ exploits the second excited level. Pulse two coupled qubits so that the |11> state briefly comes into resonance with the |02> state (one qubit's higher level). The states swap population and return, but |11> picks up a geometric phase that the other basis states do not. Timing the flux pulse to leave exactly a pi phase on |11> yields a CZ. Gate times are tens of nanoseconds.
Other realizations
- Neutral atoms: Rydberg-blockade sequences naturally give a controlled-phase gate
- Tunable couplers that turn the qubit-qubit interaction on for a set time
- Adiabatic and diabatic flux pulses that trade speed against leakage
Error sources
Because CZ uses the |02> state, leakage into that level is the main error mode, along with flux-pulse distortion and residual coupling when the gate is meant to be off. Careful pulse shaping and tunable couplers that fully switch off the interaction between gates keep both leakage and idle crosstalk low, making CZ the native two-qubit gate on many high-performing superconducting devices.