How to make an efficient mysql index for WHERE x > 0

I have a use case where my table has a couple of columns:

CREATE TABLE stocks (
    id INT,
    warehouse_id INT,
    product_id INT,
    quantity INT,
    updated_at DATETIIME
);

Almost all of my queries include WHERE quantity > 0 and ORDER BY updated_at.
eg.

WHERE quantity > 0
AND warehouse_id = 11
ORDER BY updated_at DESC

or

WHERE quantity > 0
AND product_id = 1200
ORDER BY updated_at ASC

I know I can simply add an index on quantity, but that will prevent ORDER BY from using the index.
Is there a way to make an index that only stores 2 values: quantity = 0 and quantity > 0 so I can take advantage of it with both rules I mentioned above?

eg. for queries above:

CREATE INDEX idx_test1 ON stocks ("quantity > 0", product_id, updated_at)
CREATE INDEX idx_test2 ON stocks ("quantity > 0", warehouse_id, updated_at)

Starting MySQL 8.0.13, you can create a functional index, which makes use of a function or expression.

Your pseudo-code:

CREATE INDEX idx_test1 ON stocks ("quantity > 0", product_id, updated_at);

Would translate as:

CREATE INDEX idx_test1 ON stocks ( ( quantity > 0 ), product_id, updated_at);

Expression quantity > 0 yields 1 or 0 depending on whether the condition is fulfilled - which the index uses.

It is unsure whether this will actually improve the performance of the query; 0/1 values are typically inefficient to index, because there are just two possible values. You might want to try changing the order of the columns in the index, to put a more discriminating criteria first, so maybe:

CREATE INDEX idx_test1 ON stocks ( product_id, updated_at, ( quantity > 0 ));

You might also want to have the same index with updated_at desc, if your queries use that sort direction as well.