Reversible in-place constant-depth signed-digit adder

Determine whether a constant-depth adder based on the signed-digit representation can be made both reversible and in-place.

Background

A standard route to fast single-qubit rotations is to use phase kickback from adders. Achieving constant depth with an in-place reversible adder would break an O(log log(1/epsilon)) depth barrier for certain constructions.

While constant-depth adders based on signed-digit representation exist classically, it is explicitly stated that it is unclear whether such an approach can be adapted to be both reversible and in-place, which is essential for quantum use without extraneous overhead.