in crate this feature is on our backlog as an additional aggregation function which uses the hyperlog algorithm. we plan to do the naming derived from presto http://prestodb.io/docs/current/functions/aggregate.html. Your example will then probably look like:
select approx_distinct(high_cardinality_field) from my_table
However, a possible performance improvement for one specific field per table is to cluster your table based on the high cardinality field as described under https://crate.io/docs/current/sql/ddl.html#routing