# CU3Gate¶

class CU3Gate(theta, phi, lam, label=None, ctrl_state=None)[ソース]

ベースクラス: ControlledGate

Controlled-U3 gate (3-parameter two-qubit gate).

This is a controlled version of the U3 gate (generic single qubit rotation). It is restricted to 3 parameters, and so cannot cover generic two-qubit controlled gates).

Circuit symbol:

q_0: ──────■──────
┌─────┴─────┐
q_1: ┤ U3(ϴ,φ,λ) ├
└───────────┘


Matrix representation:

\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}CU3(\theta, \phi, \lambda)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + U3(\theta,\phi,\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\th) & 0 & -e^{i\lambda}\sin(\th) \\ 0 & 0 & 1 & 0 \\ 0 & e^{i\phi}\sin(\th) & 0 & e^{i(\phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align}

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: ┤ U3(ϴ,φ,λ) ├
└─────┬─────┘
q_1: ──────■──────

$\begin{split}CU3(\theta, \phi, \lambda)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes U3(\theta,\phi,\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\th) & -e^{i\lambda}\sin(\th) \\ 0 & 0 & e^{i\phi}\sin(\th) & e^{i(\phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}$

Create new CU3 gate.

Methods Defined Here

 inverse Return inverted CU3 gate.

Attributes

condition_bits

Get Clbits in condition.

List[Clbit]

ctrl_state

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

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.

List

duration

Get the duration.

label

Return instruction label

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.

str

num_clbits

Return the number of clbits.

num_ctrl_qubits

Get number of control qubits.

The number of control qubits for the gate.

int

num_qubits

Return the number of qubits.

params

Get parameters from base_gate.

List of gate parameters.

list

CircuitError – Controlled gate does not define a base gate

unit

Get the time unit of duration.