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U3Gate

U3Gate(theta, phi, lam, label=None) GitHub(opens in a new tab)

Generic single-qubit rotation gate with 3 Euler angles.

Implemented using two X90 pulses on IBM Quantum systems:

U3(θ,ϕ,λ)=RZ(ϕπ/2)RX(π/2)RZ(πθ)RX(π/2)RZ(λπ/2)U3(\theta, \phi, \lambda) = RZ(\phi - \pi/2) RX(\pi/2) RZ(\pi - \theta) RX(\pi/2) RZ(\lambda - \pi/2)

Circuit symbol:

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

Matrix Representation:

U3(θ,ϕ,λ)=(cos(θ2)eiλsin(θ2)eiϕsin(θ2)ei(ϕ+λ)cos(θ2)) \providecommand{\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}

Examples:

U3(θ,π2,pi2)=RX(θ)U3(\theta, -\frac{\pi}{2}, \frac{pi}{2}) = RX(\theta) U3(θ,0,0)=RY(θ)U3(\theta, 0, 0) = RY(\theta)

Create new U3 gate.


Attributes

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

label

str

Return gate label

Return type

str

params

return instruction params.


Methods

add_decomposition

U3Gate.add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble

U3Gate.assemble()

Assemble a QasmQobjInstruction

Return type

Instruction

broadcast_arguments

U3Gate.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], ...]

Parameters

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

Return type

Tuple[List, List]

Returns

A tuple with single arguments.

Raises

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

c_if

U3Gate.c_if(classical, val)

Add classical condition on register classical and value val.

control

U3Gate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a (mutli-)controlled-U3 gate.

Parameters

  • 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.

Returns

controlled version of this gate.

Return type

ControlledGate

copy

U3Gate.copy(name=None)

Copy of the instruction.

Parameters

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

Returns

a copy of the current instruction, with the name

updated if it was provided

Return type

qiskit.circuit.Instruction

inverse

U3Gate.inverse()

Return inverted U3 gate.

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

is_parameterized

U3Gate.is_parameterized()

Return True .IFF. instruction is parameterized else False

mirror

U3Gate.mirror()

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

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

Returns

a fresh gate with sub-gates reversed

Return type

qiskit.circuit.Instruction

power

U3Gate.power(exponent)

Creates a unitary gate as gate^exponent.

Parameters

exponent (float) – Gate^exponent

Returns

To which to_matrix is self.to_matrix^exponent.

Return type

qiskit.extensions.UnitaryGate

Raises

CircuitError – If Gate is not unitary

qasm

U3Gate.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

U3Gate.repeat(n)

Creates an instruction with gate repeated n amount of times.

Parameters

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

Returns

Containing the definition.

Return type

qiskit.circuit.Instruction

Raises

CircuitError – If n < 1.

to_matrix

U3Gate.to_matrix()

Return a Numpy.array for the U3 gate.

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