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In TensorFlow Quantum 0.5.0, the support for Cirq gates that have arbitrary control via the gate.controlled_by function is added.

I would like to know which kind of decomposition method is used for this operation? The current decomposition seems to be efficient and any information related to that is very welcomed.

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There is no decomposition being done for controlled operations by default. The library expects whatever simulator it is using to have support for the controlled_by operation (by either decomposing it or implementing it directly). In the default C++ simulator TFQ uses qsim, controlled gates are implemented via direct application onto the state vector here

-Michael

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