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It seems that it is fairly easy to construct a unitary gate given a real unitary matrix. However, I have tried several methods with a complex unitary matrix, but they all seem to be not working. How can I construct a unitary gate in Qiskit if the matrix given is complex?

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Qiskit's class UnitaryGate accepts any unitary whether it complex or not. The following code snippet shows how to use it to construct a gate.

At first, let's generate a random unitary:

from qiskit.quantum_info import random_unitary
from qiskit.visualization import array_to_latex

n = 2
U = random_unitary(2 ** n)
array_to_latex(U)

The output will be something like

enter image description here

Now, construct the gate:

from qiskit import QuantumCircuit

# Create a QuantumCircuit that implements the unitary:
circ = QuantumCircuit(n)
circ.unitary(U, range(n))
circ.decompose().draw('mpl')

# Convert it to gate:
gate = circ.to_gate()
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