# UCGate

*class *`qiskit.circuit.library.UCGate(gate_list, up_to_diagonal=False)`

Bases: `Gate`

Uniformly controlled gate (also called multiplexed gate).

These gates can have several control qubits and a single target qubit. If the k control qubits are in the state $|i\rangle$ (in the computational basis), a single-qubit unitary $U_i$ is applied to the target qubit.

This gate is represented by a block-diagonal matrix, where each block is a $2\times 2$ unitary, that is

$\begin{pmatrix} U_0 & 0 & \cdots & 0 \\ 0 & U_1 & \cdots & 0 \\ \vdots & & \ddots & \vdots \\ 0 & 0 & \cdots & U_{2^{k-1}} \end{pmatrix}.$The decomposition is based on Ref. [1].

**References:**

**[1] Bergholm et al., Quantum circuits with uniformly controlled one-qubit gates (2005).**

Phys. Rev. A 71, 052330(opens in a new tab).

**Parameters**

**gate_list**(*list*(opens in a new tab)*[np.ndarray]*) – List of two qubit unitaries $[U_0, ..., U_{2^{k-1}}]$, where each single-qubit unitary $U_i$ is given as a $2 \times 2$ numpy array.**up_to_diagonal**(*bool*(opens in a new tab)) – Determines if the gate is implemented up to a diagonal. or if it is decomposed completely (default: False). If the`UCGate`

$U$ is decomposed up to a diagonal $D$, this means that the circuit implements a unitary $U'$ such that $D U' = U$.

**Raises**

**QiskitError** – in case of bad input to the constructor

## 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 behavioural 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 parametrised gate with a particular set of parameters for the purposes of distinguishing it in a `Target`

from the full parametrised 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.

### name

Return the name.

### num_clbits

Return the number of clbits.

### num_qubits

Return the number of qubits.

### params

return instruction params.

### unit

Get the time unit of duration.

## Methods

### inverse

`inverse()`

Return the inverse.

This does not re-compute the decomposition for the multiplexer with the inverse of the gates but simply inverts the existing decomposition.

**Return type**

### validate_parameter

`validate_parameter(parameter)`

Uniformly controlled gate parameter has to be an ndarray.