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

• URL: http://arxiv.org/abs/2102.03615v1
• Date: Sat, 6 Feb 2021 17:07:48 GMT
• Title: Halving the width of Toffoli based constant modular addition to n+3 qubits
• Authors: Oumarou Oumarou, Alexandru Paler, Robert Basmadjian
• Abstract summary: We present an arithmetic circuit performing constant modular addition having $mathcalO(n)$ depth of Toffoli gates. This is an improvement by a factor of two compared to the width of the state-of-the-art Toffoli-based constant modular adder.
• Score: 69.43216268165402
• License: http://creativecommons.org/licenses/by/4.0/
• 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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