Ph219a/CS219a
Solutions to Hw 7 May 5, 2009
Problem 1
(a) We can recall the action of the Hadamard (H = H-1 ) and the phase gates (P) on the Pauli operators from an earlier Hw problem (HW4, Problem 3a
Ph219a/CS219a
Solutions to Hw 8 May 5, 2009
Problem 1
(a) We can write Xa as a product of X 's and Z 's:
n n
Xa = (sgn)
=1
u X
=1
Z , u , v cfw_0, 1
v
(1)
Then, XA,a XB,a can be written as
n
(XA
Ph219a/CS219a
Solutions to Hw 9 June 5, 2009
Problem 1
(a) Clearly for x = 1, lnx = x - 1 = 0. Since the function f (x) = lnx is strictly concave, lnx x - 1 for x = 1, if x - 1 is a tangent at x = 1.