= Solution
The PDF circuit has its upper wire controlling both <CNOT gates>. Its successive states are
$$
|00\rangle\ \longmapsto\ \frac{|00\rangle+|10\rangle}{\sqrt2}
\ \longmapsto\ \frac{|00\rangle+|11\rangle}{\sqrt2}
\ \longmapsto\ \frac{|00\rangle+e^{2i\phi}|11\rangle}{\sqrt2}
\ \longmapsto\ \frac{|00\rangle+e^{2i\phi}|10\rangle}{\sqrt2}.
$$
The first arrow is the upper <Hadamard gate>; the middle phase arises because both ones receive a phase. The second CNOT disentangles and resets the lower wire. Hence the output is
$$
\boxed{\frac{|0\rangle+e^{2i\phi}|1\rangle}{\sqrt2}\otimes|0\rangle.}
$$
This implements doubled logical phase using two parallel <phase gates>, rather than two serial applications on one <qubit>.
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