Answer Happy

Questions 1) We primarily use the computational basis "0" and "1". We occasionally use the "+" and "-" basis. For these problems we will use the "i" and "-i" basis. These basis vectors, written in the computational basis are: | " i ") = 10) + 11) | "i") 10) 11) Show that these two basis vectors are normalized and show they are orthogonal. 2) Draw these two basis vectors on the Bloch sphere as well as drawing them in Hilbert space. 3) Write the Hadamard gate as an outer product in terms of the "i" and "-i" basis. In other words your outer product should just be in terms of ("i" |and| " ti"). 4) Calculate H| "i") and calculate H| " -i"). 5) Consider the possible quantum gate F = 0) (1 + 0) (01. Prove whether or not this represents a valid quantum logic gate. Write the Hadamard gate using the outer product representation in the "i" and "-i" basis. - -