CCY (Controlled-Controlled-Y) is a three-qubit gate: applies Y to the target qubit if both control qubits are $|1\rangle$. Like CCX, it is a doubly-controlled gate but less commonly native on quantum platforms.
Action: $|c_1 c_2 t\rangle \to |c_1 c_2 (Y|t\rangle)\rangle$ where $c_1, c_2$ are controls and $t$ is target. Applies Y only if both controls are 1.
$$\text{CCY} = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -i \\ 0 & 0 & 0 & 0 & 0 & 0 & i & 0 \end{pmatrix}$$
Basis state mapping: acts as identity on all states except $|110\rangle$ and $|111\rangle$. Maps $|110\rangle \to i|111\rangle$ and $|111\rangle \to -i|110\rangle$.
CCY can be decomposed using CCX and single-qubit gates:
$$\text{CCY} = (I \otimes I \otimes S^\dagger) \text{CCX} (I \otimes I \otimes S)$$
where $S$ and $S^\dagger$ are phase gates. Gate count: two single-qubit gates and one CCX.