CY gate

The CY gate applies a Y gate to the target qubit when the control qubit is $\vert 1 \rangle$ and leaves it unchanged when the control is $\vert 0 \rangle$. It acts on two qubits and takes no parameters. The Circuit panel draws a dot on the control wire joined to a Y box on the target wire. Measured straight away it flips the target exactly as a CX does; the phases show only once the qubits meet other gates.

Kets such as $\vert 0 \rangle$ name the basis states and rotations are described on the Bloch sphere; the qubits lesson introduces both.

Call

Matrix

The matrix uses the basis order $\vert \text{control}\;\text{target} \rangle$, that is $\vert 00 \rangle, \vert 01 \rangle, \vert 10 \rangle, \vert 11 \rangle$.

Qiskit numbers basis states with qubit 0 as the least significant bit, so Operator(CYGate()) prints the same gate in a different row and column order.

Effect on basis states

Measured straight away, CY flips the target exactly as CX does; the phases only matter once the qubits meet other gates. With the control in $\vert + \rangle$ and the target in $\vert 0 \rangle$, CY produces the entangled state $\tfrac{1}{\sqrt{2}}(\vert 00 \rangle + i\vert 11 \rangle)$.

Inverse

CY is its own inverse. Two CY gates in a row on the same control and target cancel.

Usage

from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cy(0, 1)
qc.measure([0, 1], [0, 1])

import { QuantumCircuit } from 'qiskit';

const circuit = QuantumCircuit(2, 2);
circuit.h(0);
circuit.cy(0, 1);
circuit.measure([0, 1], [0, 1]);

On a noiseless simulator every shot reads 00 or 11, in close to equal numbers.

On IonQ hardware

CY is not a native gate. It is a CX with an Sdg before it and an S after it on the target, and those two are virtual Z rotations, so CY costs the same as CX: one entangling gate (MS on Aria, ZZ on Forte) plus single-qubit pulses, before IonQ's optimiser runs. See How your circuit is compiled.

Related

• CX gate
• Y gate
• CZ gate
• Gate reference