# U3Gate

class qiskit.circuit.library.U3Gate(theta, phi, lam, label=None, *, duration=None, unit='dt')

GitHub

Bases: Gate

Generic single-qubit rotation gate with 3 Euler angles.

Warning

This gate is deprecated. Instead, the following replacements should be used

$U3(\theta, \phi, \lambda) = U(\theta, \phi, \lambda)$
circuit = QuantumCircuit(1)
circuit.u(theta, phi, lambda)

Circuit symbol:

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

Matrix Representation:

$\providecommand{\rotationangle}{\frac{\theta}{2}} U3(\theta, \phi, \lambda) = \begin{pmatrix} \cos\left(\rotationangle\right) & -e^{i\lambda}\sin\left(\rotationangle\right) \\ e^{i\phi}\sin\left(\rotationangle\right) & e^{i(\phi+\lambda)}\cos\left(\rotationangle\right) \end{pmatrix}$
Note

The matrix representation shown here differs from the OpenQASM 2.0 specification by a global phase of $e^{i(\phi+\lambda)/2}$.

Examples:

$U3(\theta, \phi, \lambda) = e^{-i \frac{\pi + \theta}{2}} P(\phi + \pi) \sqrt{X} P(\theta + \pi) \sqrt{X} P(\lambda)$$U3\left(\theta, -\frac{\pi}{2}, \frac{\pi}{2}\right) = RX(\theta)$$U3(\theta, 0, 0) = RY(\theta)$

Create new U3 gate.

## Attributes

### base_class

Get the base class of this instruction. This is guaranteed to be in the inheritance tree of self.

The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for _all_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioral perspective. In particular, you should not override base_class if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrized gate with a particular set of parameters for the purposes of distinguishing it in a Target from the full parametrized gate.

This is often exactly equivalent to type(obj), except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example:

>>> isinstance(XGate(), XGate)
True
>>> type(XGate()) is XGate
False
>>> XGate().base_class is XGate
True

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that Instruction.name should be a more suitable discriminator in most situations.

### condition

The classical condition on the instruction.

### condition_bits

Get Clbits in condition.

### 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 instruction label

### mutable

Is this instance is a mutable unique instance or not.

If this attribute is False the gate instance is a shared singleton and is not mutable.

Return the name.

### num_clbits

Return the number of clbits.

### num_qubits

Return the number of qubits.

### params

The parameters of this Instruction. Ideally these will be gate angles.

### unit

Get the time unit of duration.

## Methods

### control

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

GitHub

Return a (multi-)controlled-U3 gate.

Parameters

• num_ctrl_qubits (int) – number of control qubits.
• label (str | None) – An optional label for the gate [Default: None]
• ctrl_state (str |int | None) – control state expressed as integer, string (e.g.’110’), or None. If None, use all 1s.
• annotated (bool | None) – indicates whether the controlled gate should be implemented as an annotated gate. If None, this is set to True if the gate contains free parameters and more than one control qubit, in which case it cannot yet be synthesized. Otherwise it is set to False.

Returns

controlled version of this gate.

Return type

ControlledGate

### inverse

inverse(annotated=False)

GitHub

Return inverted U3 gate.

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

Parameters

annotated (bool) – when set to True, this is typically used to return an AnnotatedOperation with an inverse modifier set instead of a concrete Gate. However, for this class this argument is ignored as the inverse of this gate is always a U3Gate with inverse parameter values.

Returns

inverse gate.

Return type

U3Gate