It's not quite a desktop app, but the web version of Keep stays in sync with notes you makes while mobile: https://keep.google.com/.

There's also a Chrome app that wraps the site, which almost makes it feel like a real desktop app: https://chrome.google.com/webstore/detail/google-keep-notes-....

Closest you can get is keep.google.com, not a desktop app, but something you can use on the desktop...