Shor's algorithm on a nearest-neighbor machine

TL;DR

This paper presents a new quantum circuit design for implementing Shor's algorithm on a nearest-neighbor quantum computer, optimizing for linear width and quadratic depth, and explores different gate implementations.

Contribution

Introduces a novel 'nested adds' circuit for Shor's algorithm suitable for nearest-neighbor architectures, combining transform adder and approximation techniques.

Findings

Linear width and quadratic depth circuit achieved

Two versions with different gate requirements analyzed

Potential for more efficient quantum factoring implementations

Abstract

We give a new ``nested adds'' circuit for implementing Shor's algorithm in linear width and quadratic depth on a nearest-neighbor machine. Our circuit combines Draper's transform adder with approximation ideas of Zalka. The transform adder requires small controlled rotations. We also give another version, with slightly larger depth, using only reversible classical gates. We do not know which version will ultimately be cheaper to implement.