U3Gate¶

class U3Gate(theta, phi, lam, label=None)[source]

Generic single-qubit rotation gate with 3 Euler angles.

Implemented using two X90 pulses on IBM Quantum systems:

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

Circuit symbol:

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

Matrix Representation:

\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.

Attributes

 U3Gate.decompositions Get the decompositions of the instruction from the SessionEquivalenceLibrary. U3Gate.definition Return definition in terms of other basic gates. U3Gate.label Return gate label U3Gate.params return instruction params.

Methods

 U3Gate.add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction U3Gate.broadcast_arguments(qargs, cargs) Validation and handling of the arguments and its relationship. U3Gate.c_if(classical, val) Add classical condition on register classical and value val. U3Gate.control([num_ctrl_qubits, label, …]) Return a (mutli-)controlled-U3 gate. U3Gate.copy([name]) Copy of the instruction. Return inverted U3 gate. Return True .IFF. For a composite instruction, reverse the order of sub-gates. U3Gate.power(exponent) Creates a unitary gate as gate^exponent. Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. Return a Numpy.array for the U3 gate.