Here you will work through the qft, much like we did in class. we define the quantum fourier transform operator through its action on the n-qubit computational basis states: where n2" a. express uqft in dirac notation and show that it is unitary. do all the steps, like we did in class b. consider the action of uqft on an arbitrary superposition u)-σ,c ) and express the final result as iu) σ, cyl), providing an expression for ~y as we did in class, you will now reduce the state representing the action of uqft on the basis states to find how it acts on each qubit and what the circuit form 1s c. express |y) in terms of single qubit states. iyı, y2, , yn). collect the terms for each qubit, and express the rhs of eq. (1) as a tensor product of all qubits d. explicitly write out the sum on each qubit state, replace x with its binary representation ri2-) and examine the term for the kth qubit. sepa- rate the sum on in the exponent to terms that cancel out .e., that give e2irxīnte ger = 1) and terms that contribute nontrivially. keep only the latter e. is the state you found entangled or separable? f. now, imagine we do a swap operation betwee the first and n qubit, the second and (n 1)th, etc. this is the same as relabeling your qubits, so that the one you have written first is really the nth. with this swap or