Evaluate the following operations in terms of a linear combination of the 8 basis states, it is nice to write the answer in ascending order like: 000 , 001 ,..., 111 sort of like writing a vector in i j k , , order. There is no need to use any matrices but for your computational enjoyment it is true that: (3) H I I H . You know (1) H operates on qubit 1 and puts it into a linear combination of 0 and 1 , appropriately normalized. The controlled NOT operator, for example 3,2 CNOT , has 3 for the control qubit and 2 for the target qubit. If the control is 0 it leaves the target alone, if the control is 1 it flips the target. Evaluate the following expressions. Show your work. .:. a) 3,2 1,2 (3) (1) C H C H NOT NOT 010 b) 3,2 2,1 (3) (2) C H C H NOT NOT 010

3. (6 pts.) Evaluate the following operations in terms of a linear combination of the 8 basis states, it is nice to write the answer in ascending order like: 1000),|001),...,111) sort of like writing a vector in i, j, k order. There is no need to use any matrices but for your computational enjoyment it is true that: Y) = n. You know " operates on qubit 1 and puts it into a linear combination of (0) and (1), appropriately a normalized. The controlled NOT operator, for example 82), has 3 for the control qubit and 2 for the target qubit. If the control is (0) it leaves the target alone, if the control is (1) it flips the target. Evaluate the following expressions. Show your work. ... a) 322) "010) = NOT b) 8222010) = NOT NOT 3. (6 pts.) Evaluate the following operations in terms of a linear combination of the 8 basis states, it is nice to write the answer in ascending order like: 1000),|001),...,111) sort of like writing a vector in i, j, k order. There is no need to use any matrices but for your computational enjoyment it is true that: Y) = n. You know " operates on qubit 1 and puts it into a linear combination of (0) and (1), appropriately a normalized. The controlled NOT operator, for example 82), has 3 for the control qubit and 2 for the target qubit. If the control is (0) it leaves the target alone, if the control is (1) it flips the target. Evaluate the following expressions. Show your work. ... a) 322) "010) = NOT b) 8222010) = NOT NOT