$\sqrt{X}$
The $\sqrt{X}$ gate is a single-qubit unitary that squares to $X$.
$$ \sqrt{X} = \frac{1}{2}\begin{bmatrix} 1 + i & 1 - i \\ 1 - i & 1 + i \end{bmatrix} $$
Properties
- $(\sqrt{X})^2 = X$.
- Equal to $R_x(\pi/2)$ up to a global phase.
- Used as the native gate in some superconducting platforms.
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis.
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
SDK support
How to call this gate in each framework. Hover a ⓘ for a note; the support matrix compares every gate at once.
| SDK | Name |
|---|---|
| Qiskit | qiskit.circuit.library.SXGate |
| PennyLane | pennylane.SX |
| Cirq | cirq.XPowGate ⓘ |
| Q# | Std.Intrinsic.SX |
| PyQuil | — ⓘ |
| Braket | braket.circuits.gates.V ⓘ |
| BQSKit | bqskit.ir.gates.SXGate ⓘ |
| Qibo | qibo.gates.SX |
| pytket | pytket.circuit.OpType.SX |
| Stim | SQRT_X |
| OpenQASM | stdgates.inc: sx |