Halving the width of Toffoli-based constant modular addition to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math> qubits

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