Remember that Quad Touch is an engine . You must legally own the original game files (e.g., from Steam or GOG) and copy them to your device.
If you're referring to an APK (Android Package File) related to "Quad Touch" that doesn't require a license, here are some general points you might be interested in: Quad Touch Apk No License
"No License" versions cannot be updated via the Play Store. Remember that Quad Touch is an engine