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arXiv · 2102.03615

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

Oumarou Oumarou·Alexandru Paler·Robert Basmadjian
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Abstract

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.

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Oumarou Oumarou, Alexandru Paler, Robert Basmadjian. 2021-02-06. Halving the width of Toffoli based constant modular addition to n+3 qubits. https://doi.org/10.1103/physreva.105.052436

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