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

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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|i\rangle (in the computational basis), a single-qubit unitary UiU_i is applied to the target qubit.

This gate is represented by a block-diagonal matrix, where each block is a 2×22\times 2 unitary, that is

(U0000U1000U2k1).\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].


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

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


  • gate_list (list(opens in a new tab)[np.ndarray]) – List of two qubit unitaries [U0,...,U2k1][U_0, ..., U_{2^{k-1}}], where each single-qubit unitary UiU_i is given as a 2×22 \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 UU is decomposed up to a diagonal DD, this means that the circuit implements a unitary UU' such that DU=UD U' = U.


QiskitError – in case of bad input to the constructor



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)
>>> type(XGate()) is XGate
>>> XGate().base_class is XGate

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


The classical condition on the instruction.


Get Clbits in condition.


Get the decompositions of the instruction from the SessionEquivalenceLibrary.


Return definition in terms of other basic gates.


Get the duration.


Return instruction label


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.


Return the number of clbits.


Return the number of qubits.


return instruction params.


Get the time unit of duration.




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




Uniformly controlled gate parameter has to be an ndarray.

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