quantum gate directory
Square Root of X
Symbol
$\sqrt{X}$
Qubits: $1$
Description:
A gate whose square is the Pauli-$X$ (NOT) gate.
Alternate notations:
- $\sqrt{X}$
- $\mathrm{S}X$
- $V$
Controlled variant: Controlled sqrt(X)
SDK Support
| 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
|
Groups
This gate is contained in the following groups:
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.
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