Problem Set 2
CPSC 440/640 Quantum Algorithms
Andreas Klappenecker
The assignment is due Wednesday, September 20, before class.
Recall that for each unitary matrix U∈ U (2) there exist matrices A, B, C ,
and Ein U(2) such that
U
=
A
E
B C .
1) Find the matrices E,A,B,Csuch that the above ciruit realizes a con-
trolled rotation operation U= cos x−sin x
sin xcos x!.
2) Find the matrices E,A,B, and Csuch that the above circuit realizes a
controlled Hadamard gate, that is, U=H.
3) Solve Exercise 3.2 in the lecture notes.
4) Solve Exercise 3.4 in the lecture notes.
Review all material on quantum gates, teleportation, Deutsch’s problem, and
the small search algorithm.