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Quantum Computing

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  • $\begingroup$ I think that's what I was looking for. Just to make sure: Lets say the known decomposition $U=A_1 A_2 \dots A_m$ contains $C(X)$ and single qubit gates. Then for single-qubit gates we replace $A_i$ by $C(A_i)$, which is constructed following the description in N&C. And the $C(X)$ are replaced by Toffoli gates (which might also be decomposed). Right? $\endgroup$ Commented Mar 26, 2018 at 22:12
  • $\begingroup$ @M.Stern well almost. If $U$ contains a $C(X)$ (which more precisely would be a $C(X)_{ij}$, acting between $i$-th and $j$-th qubit, with $i, j>1$), then the equivalent gate in $C(U)$ is already a Toffoli gate, with first and $i$-th qubits as control and $j$-th qubit as target. You can therefore go and replace the Toffolis using the known decompositions $\endgroup$ Commented Mar 26, 2018 at 23:50