qiskit.circuit.library.U3Gate

class U3Gate(theta, phi, lam, label=None)

Generic single-qubit rotation gate with 3 Euler angles.

Implemented using two X90 pulses on IBM Quantum systems:

\[U3(\theta, \phi, \lambda) = RZ(\phi) RX(-\pi/2) RZ(\theta) RX(\pi/2) RZ(\lambda)\]

Circuit symbol:

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

Matrix Representation:

\[ \begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}U3(\theta, \phi, \lambda) = \begin{pmatrix} \cos(\th) & -e^{i\lambda}\sin(\th) \\ e^{i\phi}\sin(\th) & e^{i(\phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align} \]

Examples:

\[U3(\theta, -\frac{\pi}{2}, \frac{\pi}{2}) = RX(\theta)\]

\[U3(\theta, 0, 0) = RY(\theta)\]

Create new U3 gate.

__init__(theta, phi, lam, label=None)

Create new U3 gate.

Methods

__init__(theta, phi, lam[, label])	Create new U3 gate.
add_decomposition(decomposition)	Add a decomposition of the instruction to the SessionEquivalenceLibrary.
assemble()	Assemble a QasmQobjInstruction
broadcast_arguments(qargs, cargs)	Validation and handling of the arguments and its relationship.
c_if(classical, val)	Add classical condition on register classical and value val.
control([num_ctrl_qubits, label, ctrl_state])	Return a (mutli-)controlled-U3 gate.
copy([name])	Copy of the instruction.
inverse()	Return inverted U3 gate.
is_parameterized()	Return True .IFF.
mirror()	DEPRECATED: use instruction.reverse_ops().
power(exponent)	Creates a unitary gate as gate^exponent.
qasm()	Return a default OpenQASM string for the instruction.
repeat(n)	Creates an instruction with gate repeated n amount of times.
reverse_ops()	For a composite instruction, reverse the order of sub-instructions.
to_matrix()	Return a Numpy.array for the U3 gate.
validate_parameter(parameter)	Gate parameters should be int, float, or ParameterExpression

Attributes

decompositions	Get the decompositions of the instruction from the SessionEquivalenceLibrary.
definition	Return definition in terms of other basic gates.
duration	Get the duration.
label	Return gate label
params	return instruction params.
unit	Get the time unit of duration.

add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble()

Assemble a QasmQobjInstruction

Type renvoyé

Instruction

broadcast_arguments(qargs, cargs)

Validation and handling of the arguments and its relationship.

For example, cx([q[0],q[1]], q[2]) means cx(q[0], q[2]); cx(q[1], q[2]). This method yields the arguments in the right grouping. In the given example:

in: [[q[0],q[1]], q[2]],[]
outs: [q[0], q[2]], []
      [q[1], q[2]], []

The general broadcasting rules are:

• If len(qargs) == 1:

  [q[0], q[1]] -> [q[0]],[q[1]]
  

• If len(qargs) == 2:

  [[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]]
  [[q[0]], [r[0], r[1]]]       -> [q[0], r[0]], [q[0], r[1]]
  [[q[0], q[1]], [r[0]]]       -> [q[0], r[0]], [q[1], r[0]]
  

• If len(qargs) >= 3:

  [q[0], q[1]], [r[0], r[1]],  ...] -> [q[0], r[0], ...], [q[1], r[1], ...]
  

Paramètres

• qargs (List) – List of quantum bit arguments.

• cargs (List) – List of classical bit arguments.

Type renvoyé

Tuple[List, List]

Renvoie

A tuple with single arguments.

Lève

CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.

c_if(classical, val)

Add classical condition on register classical and value val.

control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a (mutli-)controlled-U3 gate.

Paramètres

• num_ctrl_qubits (int) – number of control qubits.

• label (str or None) – An optional label for the gate [Default: None]

• ctrl_state (int or str or None) – control state expressed as integer, string (e.g. “110”), or None. If None, use all 1s.

Renvoie

controlled version of this gate.

Type renvoyé

ControlledGate

copy(name=None)

Copy of the instruction.

Paramètres

name (str) – name to be given to the copied circuit, if None then the name stays the same.

Renvoie

a copy of the current instruction, with the name

updated if it was provided

Type renvoyé

qiskit.circuit.Instruction

property decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

property definition

Return definition in terms of other basic gates.

property duration

Get the duration.

inverse()

Return inverted U3 gate.

\(U3(\theta,\phi,\lambda)^{\dagger} =U3(-\theta,-\phi,-\lambda)\))

is_parameterized()

Return True .IFF. instruction is parameterized else False

property label

Return gate label

Type renvoyé

str

mirror()

DEPRECATED: use instruction.reverse_ops().

Renvoie

a new instruction with sub-instructions

reversed.

Type renvoyé

qiskit.circuit.Instruction

property params

return instruction params.

power(exponent)

Creates a unitary gate as gate^exponent.

Paramètres

exponent (float) – Gate^exponent

Renvoie

To which to_matrix is self.to_matrix^exponent.

Type renvoyé

qiskit.extensions.UnitaryGate

Lève

CircuitError – If Gate is not unitary

qasm()

Return a default OpenQASM string for the instruction.

Derived instructions may override this to print in a different format (e.g. measure q[0] -> c[0];).

repeat(n)

Creates an instruction with gate repeated n amount of times.

Paramètres

n (int) – Number of times to repeat the instruction

Renvoie

Containing the definition.

Type renvoyé

qiskit.circuit.Instruction

Lève

CircuitError – If n < 1.

reverse_ops()

For a composite instruction, reverse the order of sub-instructions.

This is done by recursively reversing all sub-instructions. It does not invert any gate.

Renvoie

a new instruction with

sub-instructions reversed.

Type renvoyé

qiskit.circuit.Instruction

to_matrix()

Return a Numpy.array for the U3 gate.

property unit

Get the time unit of duration.

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression