  We present an arithmetic circuit performing constant modular addition having
$\mathcal{O}(n)$ depth of Toffoli gates and using a total of $n+3$ qubits. This
is an improvement by a factor of two compared to the width of the
state-of-the-art Toffoli-based constant modular adder. The advantage of our
adder, compared to the ones operating in the Fourier-basis, is that it does not
require small angle rotations and their Clifford+T decomposition. Our circuit
uses a recursive adder combined with the modular addition scheme proposed by
Vedral et. al. The circuit is implemented and verified exhaustively with
QUANTIFY, an open-sourced framework. We also report on the Clifford+T cost of
the circuit.
