What is the cost of turning a $U$ circuit into a $CU$ circuit? (add a control to it)
- The circuit operates on a register of length $q$
- Suppose the number of quantum gates is $l(U)$
- Suppose the depth of the circuit is $d(U)$
- Suppose the classical cost of the circuit construction is $T(U)$
So basically my question is - given such a $U$ what are the
$T(CU)$, $l(CU)$, $d(CU)$?
and for $C^kU$?
$T(C^kU)$, $l(C^kU)$, $d(C^kU)$?
O notation is also good)