quantum gate directory
Controlled sqrt(X)
Symbol
$\mathrm{C}\sqrt{X}$
Description:
Applies $\sqrt{X}$ to the target when the control qubit is $|1\rangle$.
Alternate notations:
- $\mathrm{CS}X$
- $\mathrm{C}V$
- $\text{controlled-}\sqrt{X}$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.CSXGate
|
| PennyLane | — |
| Cirq | — |
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
The controlled-$\sqrt{X}$ gate applies $\sqrt{X}$ to the target qubit conditioned on the control being $|1\rangle$.
$$ \mathrm{C}\sqrt{X} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \frac{1 + i}{2} & \frac{1 - i}{2} \\ 0 & 0 & \frac{1 - i}{2} & \frac{1 + i}{2} \end{bmatrix} $$
Properties
- $(\mathrm{C}\sqrt{X})^2 = \mathrm{C}X$, but there are other gates $A$ that satisfy $A^2 = \mathrm{C}X$ such as $(\mathrm{C}\sqrt{X})^\dag$.
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