A 2D Nearest-Neighbor Quantum Architecture for Factoring in Polylogarithmic Depth

TL;DR

This paper presents a 2D nearest-neighbor quantum architecture for Shor's algorithm that achieves polylogarithmic depth, significantly improving circuit depth at the expense of increased size and width.

Contribution

It introduces a novel 2D nearest-neighbor quantum architecture with constant-depth subroutines and a new model allowing classical control and parallel modules for efficient factoring.

Findings

Achieves $O( ext{log}^2(n))$ circuit depth for factoring

Provides a new constant-depth quantum unfanout circuit

Demonstrates exponential depth improvement over previous methods

Abstract

We contribute a 2D nearest-neighbor quantum architecture for Shor's algorithm to factor an $n$-bit number in $O(\log^2(n))$ depth. Our implementation uses parallel phase estimation, constant-depth fanout and teleportation, and constant-depth carry-save modular addition. We derive upper bounds on the circuit resources of our architecture under a new 2D nearest-neighbor model which allows a classical controller and parallel, communicating modules. We also contribute a novel constant-depth circuit for unbounded quantum unfanout in our new model. Finally, we provide a comparison to all previous nearest-neighbor factoring implementations. Our circuit results in an exponential improvement in nearest-neighbor circuit depth at the cost of a polynomial increase in circuit size and width.