Identify identical geometry in column with common number in QGIS?

I'm trying to identify identical (or duplicate) geometry in QGIS by adding a common number for each identical set. For example, if there are 4 features, and 2 are identical:

1| Identical with 2

2| Identical with 1

3|

4|

I want the following:

1|1

2|1

3|2

4|3

With ArcGIS, there is a tool called "Find Identical" that creates a table for geometry duplicates - you choose a shapefile and choose "Shape" under the list to identify within, and it produces a table of identicals, as above. Here is a screenshot of the tool: