Hello,

It may be a nitpick, but i think there is an error in the definition of the error metric. In general the difference of two unitary operators may not be diagonalizable, so the error may differ from the biggest eigenvalue. You probably mean something like $|A| = max_{v \neq 0} \frac{|Av|}{|v|}$ which is equal to the definition stated if $A$ can be diagonalized.

Or maybe actually all operators of the form $U - U’$ can be diagonalized and I’m gravely wrong here.