Is there a standard date format that expresses Quarters?

What date format would you use to express a quarter, that is still recognized as a date format?

For example I have spreadsheet of rows with a date column with dates in YYYY-MM-DD format.

I want to transform the data, grouping by quarter, counting the rows in each quarter.

The output would be something like

Q4-2017, 403
Q1-2018, 298
Q2-2018, 139

But I want to then filter down that list to only this year etc.

What format would you use for the resulting date column that expresses the quarter, while still being a recognized date format?

From my research it seems like you would need to have 2 date columns in order to express a time period. But was wondering if I am missing something.