If I have a quantum gate, how can I get the gate that represents half-way of that gate? As an example of what I want: How do I derive $\sqrt {SWAP} $ gate
$$\sqrt {SWAP} = \left( {\matrix{ 1 & 0 & 0 & 0 \cr 0 & {{{1 + i} \over 2}} & {{{1 - i} \over 2}} & 0 \cr 0 & {{{1 - i} \over 2}} & {{{1 + i} \over 2}} & 0 \cr 0 & 0 & 0 & 1 \cr } } \right)$$ from $SWAP$ gate? $$SWAP = \left( {\matrix{ 1 & 0 & 0 & 0 \cr 0 & 0 & 1 & 0 \cr 0 & 1 & 0 & 0 \cr 0 & 0 & 0 & 1 \cr } } \right)$$
