# How to get half-way gate of a two-qubit quantum gate? [duplicate]

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? $$SWAP = \left( {\matrix{ 1 & 0 & 0 & 0 \cr 0 & 0 & 1 & 0 \cr 0 & 1 & 0 & 0 \cr 0 & 0 & 0 & 1 \cr } } \right)$$

• by "half-way" gate do you just mean square root? Oct 27 '21 at 15:26
• Many versions of this question have been asked. (I asked one myself recently!) But I like in particular this one. Oct 27 '21 at 16:20
• Thank you all for your attention. The answer that Mark S attached is exactly what I was looking for. Oct 27 '21 at 16:32