Assignment 1 Due Wednesday October 4, in class.
(a) (Practice with bra-ket notation) A is a measurement (Hermitian) operator with eigenvectors
yi
eigenvalues li.
Show that the expected value of a measurement with A when the system is in state
y is
Si
li
|<yi|y>|2
= <y|A|y>
(b) (Practice with single-qubit gates) Let H be the Hadamard gate, and
f the phase gate, defined by the 2x2 matrix
1 0
0 exp(if)
normalized by 1/Ö2. Show that you can generate
the most general state of a single qubit by operating on <0| with H,
followed by a phase gate, followed by an H, followed by a phase gate. The
phases of the phase gates are for you to determine.