# CSXGate¶

class CSXGate(label=None, ctrl_state=None)[Quellcode]

Bases: qiskit.circuit.controlledgate.ControlledGate

Controlled-√X gate.

Circuit symbol:

q_0: ──■──
┌─┴──┐
q_1: ┤ √X ├
└────┘


Matrix representation:

$\begin{split}C\sqrt{X} \ q_0, q_1 = I \otimes |0 \rangle\langle 0| + \sqrt{X} \otimes |1 \rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & (1 + i) / 2 & 0 & (1 - i) / 2 \\ 0 & 0 & 1 & 0 \\ 0 & (1 - i) / 2 & 0 & (1 + i) / 2 \end{pmatrix}\end{split}$

Bemerkung

In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q_1. Thus a textbook matrix for this gate will be:

     ┌────┐
q_0: ┤ √X ├
└─┬──┘
q_1: ──■──

$\begin{split}C\sqrt{X}\ q_1, q_0 = |0 \rangle\langle 0| \otimes I + |1 \rangle\langle 1| \otimes \sqrt{X} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & (1 + i) / 2 & (1 - i) / 2 \\ 0 & 0 & (1 - i) / 2 & (1 + i) / 2 \end{pmatrix}\end{split}$

Create new CSX gate.

Attributes

ctrl_state

Return the control state of the gate as a decimal integer.

Rückgabetyp

int

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates. If the gate has open controls, as determined from self.ctrl_state, the returned definition is conjugated with X without changing the internal _definition.

Rückgabetyp

List

duration

Get the duration.

label

Return instruction label

Rückgabetyp

str

name

Get name of gate. If the gate has open controls the gate name will become:

<original_name_o<ctrl_state>

where <original_name> is the gate name for the default case of closed control qubits and <ctrl_state> is the integer value of the control state for the gate.

Rückgabetyp

str

num_ctrl_qubits

Get number of control qubits.

Rückgabe

The number of control qubits for the gate.

Rückgabetyp

int

params

Get parameters from base_gate.

Rückgabe

List of gate parameters.

Rückgabetyp

list

Verursacht

CircuitError – Controlled gate does not define a base gate

unit

Get the time unit of duration.