Factoring $2048$ bit RSA integers with a half-million-qubit modular atomic processor

TL;DR

This paper demonstrates that a distributed, modular atomic quantum processor can efficiently factor 2048-bit RSA integers using Shor's algorithm, with minimal performance overhead compared to a single-module system.

Contribution

It provides the first end-to-end compilation, optimization, and simulation framework for large-scale quantum integer factorization on modular atomic hardware.

Findings

2048-bit RSA integers can be factored in only 16% more time on a modular processor.

A half-million-qubit modular atomic processor with specific communication and measurement capabilities is feasible.

The work offers a blueprint for designing large-scale modular quantum algorithms.

Abstract

Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many modules. In this paper, we provide a distributed compilation of Shor's algorithm on a modular atomic processor. We present an end-to-end compilation and optimization strategy that focuses on the interplay between the inter-module communication and the intra-module clock rate. With a half-million-qubit modular atomic processor with a communication rate of $10^5$ Bell pairs per second and a measurement time of 1 ms in a CPU-inspired architecture, we demonstrate that 2048-bit RSA integers can be factored in only 16\% more time than a single-module architecture. Our work presents the first end-to-end analysis and simulation of large-scale integer factorization on modular atomic hardware and it provides a blueprint for the future design of other large-scale modular algorithms.