This is a tricky undocumented parameter. You will only find references for that in the Chrome(ium) developers community. My answer is based on some Google Searches only so maybe someone from inside will help further.

AQS stands for Assisted Query Stats and is a string parameter

It's "used for logging purposes" as you can find in some commenting in this code.

It "contains impressions of all autocomplete matches shown at the query submission time".

It doesn't look like that this would be used to uniquely identify a browser, but this is only speculation as the documentation appears to be closed for Google people (if you follow the URL pointed in this same code comment).

Finally, just to point to more background on the lack of documentation, there is this SO question and this curious comment from a Chrome developer in this thread about AQS implementation: "the comment here is both too short and confusing. Perhaps a longer explanation of what AQS is, what the constraints on it are, and why those constraints are necessary, should be added to some canonical place that talks about AQS."

That's it, if the documentation was created it's not Google findable.