Hi, waichuen.
I see that you'd like to use the new features in the Notes application but it's not working with the notes you store in your Google account. I'm happy to help.
Use Notes on your iPhone, iPad, and iPod touch -- If the email provider doesn't support these new features, you can use iCloud instead, and still sync them across your devices.
Get started
- Make sure that your iPhone, iPad, or iPod touch has the latest version of iOS.
- To use the latest features of Notes, make sure that you set up Notes with iCloud or have notes saved on your device. Many Notes features won't work with other email providers.
Take care!