3. Decoherence-free subspace 3 marks (a) Find a basis for a two-dimensional subspace of two qubits that is not affected by the phase noise operation p > Us & UpU, & U., where Uo = R= (0) = e -10/2 0 - O 10/2 In other words, find two orthogonal 2-qubit states (do) and ($1) such that, for i =0,1, U. @ Veldi) = elaldi) where o is a constant. (b) Describe how to implement the logical X gate in the basis where |do) is the logical '0' and (01) is the logical '1'. (c) Also describe how to implement a logical Z gate