Consider running Simon$$s algorithm on the following function acting on $3$ bits:

f$(000)=101$

f$(001)=011$

f$(010)=001$

f$(011)=110$

f$(100)=101$

f$(101)=011$

f$(110)=001$

f$(111)=110$

$($a$)$ What is the period a$?$

$($b$)$ What is the state after the first set of Hadamards?$($c$)$ What is the state after applying the function f$($x$)?$

$($d$)$ When the output register is measured, if the outcome is $011,$ what is the state of the

input register?

$($e$)$ What is the state after the second set of Hadamards?