Abstract
We present an arithmetic circuit performing constant modular addition having $O(n)$ 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 $\text{Clifford}+T$ 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 $\text{Clifford}+T$ cost of the circuit.
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