quantum gate directory
Controlled-Y
Symbol
$\mathrm{C}Y$
Qubits: $2$
hermitian
Description:
Applies $Y$ to the target qubit when the control qubit is in the $|1\rangle$ state.
Alternate notations:
- $\Lambda(Y)$
- $\text{controlled-}Y$
Controlled version of: Pauli-Y
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.CYGate
|
| PennyLane |
pennylane.CY
|
| Cirq |
cirq.CY
|
| Q# |
Std.Canon.CY
|
| PyQuil | — ⓘ |
| Braket |
braket.circuits.gates.CY
|
| BQSKit |
bqskit.ir.gates.CYGate
|
| Qibo |
qibo.gates.CY
|
| pytket |
pytket.circuit.OpType.CY
|
| Stim |
CY
|
| OpenQASM |
stdgates.inc: cy
|
Groups
This gate is contained in the following groups:
The controlled-$Y$ gate is a two-qubit entangling gate that conditionally applies $Y$ to the target.
$$ \mathrm{C}Y = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & -i \\ 0 & 0 & i & 0 \end{bmatrix} $$
Properties
- Clifford, Hermitian, and self-inverse.
- Related to CNOT by $S$ gates on the target: $\mathrm{C}Y = (I \otimes S)\,\mathrm{CNOT}\,(I \otimes S^\dagger)$.
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