based $$on $$this $$diagram $$answer$.$

$4$

$$options $$are $$given $$please

choose $$right $$one$.$this $$is $$a $$quatuam $$computing $$problem$.$intial $$states $$are $$given $$but $$your $$goal $$is $$to $$find $$final $$state$.$when $$following $$q $$values $$are $$passed $$through $$this $$circuit i$)$if q$0=1$ and q$1=1$:

$1/2(100>-|10>-|01>+|11>$

$1/21-100>+|10>+|01>-|11>)$

$1/2(100>+|10>+|01>+|11>)$

$-11>$

ii$)$ if q$0=0$ q$1=0$

$|11>01/2(100>+|102+1012+/113)$

$100>$

$1/2(-|00>+|10>+|01>-|11>$

$)$

iii$)$ q$0=0$ q$1=1$

$110>$

$1/2(|00>+|10>+|01>+|11>)$

$101>$

$1/2(100>-|10>-|01>+|11>)$

iv$)$if q$0=1$ and q$1=0$

$1/2(|00>+|10>+|01>+|11>)$

$101>$

$<mn\; id="EditorElement\_1881477">1</mn><mn\; id="EditorElement\_1881478">0</mn><mi\; id="EditorElement\_1881479">|</mi>$

$1/2(|00>-|10>-|01>+|11>)$

v$)$if q$0=0$ q$1=0$

$1/2(|00>+|10>+|01>+|11>)$

$1/2(|00>+|10>-|01>+|11>)$

$1/2(|00>+|10>+|01>-|11>)$

$1/2(|00>-|10>+|01>+|11>)$

vi$)$q$0=0,$ q$1=1$

$1/2|00>+|10>-|01>+|115$

$1/2(100>-|10>+|01>+|11>)$

$1/2(100>+|10>+|01>-|11>)$

$1/2(|00>+|10>+|01>+|11>)$

vii$)$ if q$0=1$ q$1=0$

$1/2(|00>+|10>+|01>+|11>)$

$1/2(|00>+|10>-|01>+|11>)$

$1/2(100>-|10>+|01>+|11>)$

$1/2(100>+|10>+|01>-|11>)$

viii$)$q$0=1$ q$1=1$

$1/2(|00>+|10>+|01>+|11>)$

$1/2(100>-|10>-|01>-|11>)$

$1/2(100>+|10>+|01>-|11>)$

$1/2(-|00>+|10>+|01>-|11>)$