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

TL;DR

This paper introduces a more width-efficient Toffoli-based constant modular addition circuit with linear depth and minimal qubit usage, avoiding complex rotations and decompositions, verified through simulation.

Contribution

It presents a novel modular addition circuit with halved width compared to previous Toffoli-based designs, using recursive methods and verified with QUANTIFY.

Findings

Achieves $ ext{O}(n)$ depth with $n+3$ qubits

Reduces circuit width by a factor of two

Eliminates need for small angle rotations and T decomposition

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.