What is the controlled-phase gate?

What is the controlled-phase gate?

The controlled-phase gate, also known as the controlled-Z gate or CPHASE gate, is a two-qubit quantum gate that applies a phase shift to the target qubit based on the state of the control qubit. It performs a conditional phase shift operation, where the phase of the target qubit is flipped if and only if the control qubit is in the state |1⟩. The controlled-phase gate is commonly represented by the matrix:

|1 0 0 0|
|0 1 0 0|
|0 0 1 0|
|0 0 0 -1|

This gate is a fundamental building block in quantum algorithms and quantum error correction codes.