The qt4-demos package should provide the qtdemo application, yet it is missing after installing the qt4-demos package.
$ qtdemo
The program 'qtdemo' is currently not installed. You can install it by typing:
sudo apt-get install qt4-demos
ProblemType: Bug
DistroRelease: Ubuntu 13.04
Package: qt4-demos 4:4.8.4+dfsg-0ubuntu9
ProcVersionSignature: Ubuntu 3.8.0-19.29-generic 3.8.8
Uname: Linux 3.8.0-19-generic x86_64
ApportVersion: 2.9.2-0ubuntu8
Architecture: amd64
Date: Sat Apr 27 10:32:11 2013
InstallationDate: Installed on 2013-02-13 (72 days ago)
InstallationMedia: Ubuntu 12.10 "Quantal Quetzal" - Release amd64 (20121017.5)
MarkForUpload: True
ProcEnviron:
TERM=xterm
PATH=(custom, no user)
XDG_RUNTIME_DIR=<set>
LANG=en_US.UTF-8
SHELL=/bin/bash
SourcePackage: qt4-x11
UpgradeStatus: Upgraded to raring on 2013-04-03 (23 days ago)
Status changed to 'Confirmed' because the bug affects multiple users.