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About algassert.com

I've been thinking about circuit constructions lately, and the question occurred to me: if circuit $A$ uses $O(N)$ gates and circuit $B$ uses $O(N^2)$ gates, but in parallel and with a better constant factor so that $B$'s depth is a bit better than $A$'s, would you ever use $A$ instead of $B$? Can lowering the width (i.e. number of operations being applied in parallel on average) of a circuit ever justify increasing the depth?

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