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# CRXGate¶

class CRXGate(theta, label=None, ctrl_state=None)[fuente]

Bases: ControlledGate

Controlled-RX gate.

Can be applied to a QuantumCircuit with the crx() method.

Circuit symbol:

q_0: ────■────
┌───┴───┐
q_1: ┤ Rx(ϴ) ├
└───────┘


Matrix representation:

\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}CRX(\theta)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + RX(\theta) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos{\th} & 0 & -i\sin{\th} \\ 0 & 0 & 1 & 0 \\ 0 & -i\sin{\th} & 0 & \cos{\th} \end{pmatrix}\end{split}\end{aligned}\end{align}

Nota

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: ┤ Rx(ϴ) ├
└───┬───┘
q_1: ────■────

\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}CRX(\theta)\ q_1, q_0 = |0\rangle\langle0| \otimes I + |1\rangle\langle1| \otimes RX(\theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos{\th} & -i\sin{\th} \\ 0 & 0 & -i\sin{\th} & \cos{\th} \end{pmatrix}\end{split}\end{aligned}\end{align}

Create new CRX gate.

Methods Defined Here

 inverse Return inverse CRX gate (i.e.

Attributes

condition_bits

Get Clbits in condition.

Tipo del valor devuelto

List[Clbit]

ctrl_state

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

Tipo del valor devuelto

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.

Tipo del valor devuelto

List

duration

Get the duration.

label

Return instruction label

Tipo del valor devuelto

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.

Tipo del valor devuelto

str

num_clbits

Return the number of clbits.

num_ctrl_qubits

Get number of control qubits.

Devuelve

The number of control qubits for the gate.

Tipo del valor devuelto

int

num_qubits

Return the number of qubits.

params

Get parameters from base_gate.

Devuelve

List of gate parameters.

Tipo del valor devuelto

list

Muestra

CircuitError – Controlled gate does not define a base gate

unit

Get the time unit of duration.