WWDC 2012 Session 208 is about UIKit state preservation and restoration. Pretty much at the end the debugging tool "Restrospector" is mentioned. It should visualize the persisted state on disk.
The state itself is persisted to the file "data.data" in the "Saved Application State" directory. When you open it, it's an XML file, but part of it are not human readable.
I did search the Apple developer forums and developer site, but there were only people asking for this tool as well, but nobody had an answer. Maybe Stack Overflow can help?
I was wondering the same thing, and today I found something similar on the Apple Developer Downloads page. It's called the "restorationArchiveTool for iOS 7".
Put restorationArchiveTool in your path and you can invoke it like so:
restorationArchiveTool --plist --structured -o ~/path/to/output.file ~/Library/Application\ Support/iPhone\ Simulator/{VERSION}/Applications/{HASH}/Library/Saved\ Application\ State/your.bundle.identifier.savedState
The tool also comes with a DebugLogging and DeveloperMode mobileconfig, but I couldn't get those to install properly.