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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. Thisis an improvement by a factor of two compared to the width of thestate-of-the-art Toffoli-based constant modular adder. The advantage of ouradder, compared to the ones operating in the Fourier-basis, is that it does notrequire small angle rotations and their Clifford+T decomposition. Our circuituses a recursive adder combined with the modular addition scheme proposed byVedral et. al. The circuit is implemented and verified exhaustively withQUANTIFY, an open-sourced framework. We also report on the Clifford+T cost ofthe circuit.

Halving the width of Toffoli based constant modular addition to n+3 qubits