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cirq.Ry is a method that, given an angle, returns a gate. You then apply the gate to a qubit: cirq.Ry(angle).on(qubit) or, equivalently but a bit more confusingly: cirq.Ry(angle)(qubit)


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If you call initialize in this case, you will be specifying a general state in $\mathbb{C}^8$. However what you have is more specialized. For example only having 4 nonzero amplitudes. So the call to initialize won't know this a priori. So it won't realize the initialization circuit can be decomposed easily. Or at least it will need to do some extra ...


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You can initialize a quantum state by using the QuantumCircuit.initialize() function. For example, to initialize a circuit into the state |1>, we can perform the initialization as follows : vector = [0,1] qr = QuantumRegister(1) qc = QuantumCircuit(qr) qc.initialize(vector, [qr[0]]) There is more detail about how to use it in this tutorial


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