Symptoms
When you use DBCC CLONEDATABASE to clone a database that has query store functionality enabled in SQL Server 2016 Service Pack 1 (SP1), the runtime cache of the query store does not copy to the clone.
Resolution
This fix is included in Cumulative Update 2 for SQL Server 2016 Service Pack 1.
Status
Microsoft has confirmed that this is a problem in the Microsoft products that are listed in the "Applies to" section.
References
Learn about the terminology that Microsoft uses to describe software updates.