No, nobody uses quantum-proof encryption yet (usually called post-quantum encryption). Google and others have experimented with it for https and it worked fine, but nothing is deployed yet and standardization has barely began. So if someone records your traffic today, they will be able to decrypt it in a couple of decades.
> Google and others have experimented with it for https and it worked fine
To be clear, Google didn't experiment with actually using post-quantum crypto. Their experiment was to figure out what was the largest key sizes that browsers and networks would accept before you start degrading connections. Their "post-quantum keys" were just padding bytes. This was gone through in the Bernstein and Lange talk this year at 35C3[1]. This is a good thing, given the history of the security of post-quantum candidates[2].
