Congrats this looks like a nice browser. Is there a way to synchronize the browsers across devices?
Not yet. That will be coming.
No official sync. There's kind of work around - I keep my Bookmarks and Notes files in google drive and keep them in sync between PCs($HOME/.config/vivaldi/Default is their directory on Linux and there is vivaldi/Default dir somewhere in %UserDir%/AppData on Windows).
Semi-brilliant idea! Anyone can use one of the free cloud sync services, install it on all relevant devices, and sync the relevant file to the cloud. Kewl.