  We present a novel set of reversible modular multipliers applicable to
quantum computing, derived from three classical techniques: 1) traditional
integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction.
Each multiplier computes an exact result for all binary input values, while
maintaining the asymptotic resource complexity of a single (non-modular)
integer multiplier. We additionally conduct an empirical resource analysis of
our designs in order to determine the total gate count and circuit depth of
each fully constructed circuit, with inputs as large as 2048 bits. Our
comparative analysis considers both circuit implementations which allow for
arbitrary (controlled) rotation gates, as well as those restricted to a typical
fault-tolerant gate set.
