Problem Set 2
CPSC 629 Analysis of Algorithms
Andreas Klappenecker
The assignment is due next Wednesday, before class.
Solve exercises 2.14 – 2.27 given in the lecture notes. Give concise and clear
answers. Give complete proofs.
Read pages 1–28 in Nielsen and Chuang. Pages 13–28 are important; pages
1–12 make good beadtime reading. If you need further motivation: These
pages contain the anwer to at least one homework question!
Common problems in the previous homework:
•If φis a real number, then eiφ = cos φ+isin φ. Any such number
satisfies |eiφ|2= 1.
•A matrix Uis unitary if and only if hUx|Uyi=hx|yifor al l x, y ∈Cm.
It is not sufficient to check this just for a special case, such as y=x,
unless you prove that.
•Make sure that you know what you want to prove! Learn and under-
stand the definitions first, then try to prove the result.
•Do not write excessively long answers! Keep it succinct and clear.
Please note the following correction:
Exercise 2.27 Design a quantum circuit that implements the parity function
f(x2, x1, x0) = x2⊕x1⊕x0. Show how this circuit can be used to generate
the state 1
2(|0000i+|1010i+|1100i+|0110i).
Assume that the input is |0000i. You can use additional single qubit gates
to obtain this result.