What is the controlled-controlled-S gate?

What is the controlled-controlled-S gate?

The controlled-controlled-S gate, also known as the Toffoli gate or the CCNOT gate, is a three-qubit gate in quantum computing. It performs a controlled-NOT operation on the target qubit if and only if both control qubits are in the state |1⟩. In other words, if the first two qubits are in the state |1⟩, the third qubit is flipped, otherwise, it remains unchanged. This gate is a fundamental building block for various quantum algorithms and circuits.