Qubit permutation with circuits. (a) What does the two-qubit circuit (CX)(CX)[20,1](CX) do to the two qubits? (b) Let d be a positive integer. Factor the d-bit-reversal permutation matrix Pd into a product of at most 3d/2 extensions of two-qubit gates. Hints: For part (a), you may want to draw the two-qubit circuit. What does the corresponding classical circuit do? Verify that your intuition is correct by evaluating the circuit for the vectors 00,01,10, and 11 in the computational basis. For part (b), recall the d-bit-reversal permutation matrix Pd from Week 2. To factor Pd, you may want to use part (a) extended to qubits j and d1j for j=0,1,,d/21