QC 11 and later (up to latest version 11.52) still do NOT run on IE-64bit, only IE-32 (QC11 currently supports IE-32 v7-9, and IE-32 v10 with ALM Patch 14).
QC11.52 supports IE 8 and 9 so far (32-bit).
On a Win7/64 machine, the default IE (shortcut or in the first-level of the start-menu) is usually the 32-bit version, and users have to specifically find and launch the 64-bit one.
Anyway, you must launch the 32-bit version of IE on the PC (with ''Run as Administrator'' the first time), go to the QC URL. As it loads various stuff for the QC ''client'' , it might land on a Microsoft download page for Visual C++ Redistributable -- choose the 32-bit/X86 version (it will NOT WORK with the 64-bit one).
If the user has already tried launching QC from the 64-bit IE, it might start working after loading again from IE-32, if not, you will need to uninstall ALM client from that person's PC.
Directions to manually uninstall ALM client here (you need an HP Passport account to see the page):
HP Software Knowledge Document KM1400062 (http://support.openview.hp.com/selfsolve/document/KM1400062)
Get ALM uninstaller here (you need an HP Passport account to see the page):
HP Software Knowledge Document KM1400068 (http://support.openview.hp.com/selfsolve/document/KM1400068)