iOS screen mirroring via USB to a Windows PC?
The HDMI or VGA adapter that can be purchased from Apple allows mirroring to an external monitor, projector or other display that allows video IN.  Does your PC allow video in via HDMI?  (I'm not aware of any that do, most are video OUT)  There is a 3rd party application called Duet that allows your iOS device to be used as an external or second monitor via USB but I think that is the opposite of what you are trying to accomplish based on your question.  The screenshot shows Duet for Mac but there is a PC version as well.

From the Apple documentation regarding cable:


  Use the Lightning to VGA Adapter with your iPad with Retina display, iPad mini, iPhone 5, and iPod touch (5th generation) with Lightning connector. The Lightning to VGA Adapter supports mirroring of what is displayed on your device screen including apps, presentations, websites, slideshows, and more — to your VGA-equipped TV, display, projector or other compatible display in up to 1080p HD.
  It also outputs video content - movies, TV shows, captured video- to your big screen in up to 1080p HD. Simply attach your Lightning to VGA Adapter to the Lightning connector on your device and then to your TV or projector via a VGA cable (sold separately).


Apple Store Link

Duet:


UPDATE:  This may or may not be useful, but this article mentions a method that may suit your needs.  From the article:


  Apowersoft Phone Manager
  It is completely compatible with iOS and Android operation system. To learn how to display iPad on computer, get started with the following steps.
  Download this tool and connect iPad to computer through USB cable.