Make ControlledGate work with gates that only provide a decomposition

The following should work:

import cirq


class G(cirq.TwoQubitGate):
    def _decompose_(self, qubits):
        a, b = qubits
        yield cirq.X(a)**0.5
        yield cirq.H(b)
        yield cirq.CZ(a, b)


cg = cirq.ControlledGate(G())
x, y, z = cirq.LineQubit.range(3)
c = cirq.Circuit.from_ops(cg(x, y, z))
print(c.to_unitary_matrix())

but currently it raises an exception:

Operation without a known matrix or decomposition: cirq.ControlledGate(sub_gate=[...G...].on(cirq.LineQubit(0), cirq.LineQubit(1), cirq.LineQubit(2))

because ControlledGate doesn’t have a _decompose_ method. This issue is to add that method.

[vtomole]

@balopat Go for it 😃

[Strilanc]

This ended up being more complicated than I expected, because it requires defining a controlled operation and understanding how the decomposition machinery works in detail.

    def _decompose_(self, qubits):
        control_qubit = qubits[0]
        result = protocols.decompose_once_with_qubits(self.sub_gate,
                                                      qubits[1:],
                                                      NotImplemented)
        if result is NotImplemented:
            return NotImplemented
        for op in result:
            yield ControlledOperation(control_qubit, op)