Comments (1)
No, that is correct. The synthesis algorithm dbs
is a generic heuristic, which does not know that the given permutation is a Fredkin gate in this case. It does not optimise for CNOT count. For the Fredkin gate one could try using algorithms such as SAT-based CNOT+Rz synthesis described in this paper. For this technique one needs to first break down the gate into a phase polynomial representation + H gates.
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