There are no known issues running Quality Center 12.5x on Microsoft Azure. The official statement from HP on Virtual Environments (below) states that as long as the Virtual Environment supports the physical system requirements of the product, it should be fine.

Orasi Software provides ALM/QC hosting services powered by Microsoft Azure. I would recommend taking a look at this option as well. This would allow Orasi to take ownership of the setup and maintenance of the server and allow your organization to focus on testing.

**Orasi Hosting with Azure:**

http://www.orasi.com/testing-solutions/Pages/Hosting.aspx

**HP Statement concerning supporting Virtual Environments:**

HP ALM/QC is certified to work with VMWare ESX/ESXi. Due to the rapidly evolving architectures provided by virtualization vendors ( e.g. Hyper V or Citrix) as long as the above stated vendor guarantees full compatibility of the virtualized environment to the HP ALM/QC approved system requirements for physical hardware, HP ALM/QC will support the virtualized environments and function as designed.