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How to construct Control-Z with square root of swap?

Quantum Computing Asked by Dingshan Liu on December 12, 2020

How to construct Control-Z with square root of swap(up to some single qubit operations)? In some papers it just directly mention that it’s possible but didn’t tell how to do.

2 Answers

Found by just trying stuff in Quirk:

cz from sqrt swap

Answered by Craig Gidney on December 12, 2020

To add to the circuit by @Craig, the reason why papers tend to mention that some gate is obtainable by $sqrt{swap}$ upto a few single qubit gates is because the set that contains the $sqrt{swap}$ gate and all the one qubit gates is considered to be a universal set of quantum gates. That is, by just using just the $sqrt{swap}$ gate and some single qubit gates, it is possible to construct any single or multi qubit quantum gate.

Answered by Tharrmashastha V on December 12, 2020

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