2. The matrix for a controlled not is: 11 00 CNOT = 0 1 0 0 0 1 0 0 0 0 0 0 1 Show that the CNOT gate is reversible. Hint: CNOT is its own inverse. Let 0,91) = [90 91 92 9]" be some qubit pair. Apply NOT to this twice and show that the result is 60,61). 3. Verify that NOT 0,y) 10,y) and that NOT1, y) = [1, not y), for y = 10) and y = 11). 4. What is NOT 98 +), 1)? 5. What is CNOT", 19+)? 6. Let U be a single qubit gate with matrix a C and let y be the qubit [yo y]. What is U (y)? If gate U is as defined above then a controlled U gate has matrix [1 0 0 0 CU= 0 1 0 a 0 0 0 0 0 b d c Show that this controlled U gate does implement: if (x == 0) { 0,y: } else { 1,2(y); }