A Rydberg-atom approach to the integer factorization problem

TL;DR

This paper presents a novel quantum computing approach using Rydberg atoms to factor small integers, demonstrating the potential and limitations of this method for solving the integer factorization problem.

Contribution

It introduces a Rydberg-atom-based quantum algorithm for factorization and experimentally demonstrates its application on small composite numbers.

Findings

Successfully factored small numbers like 6, 15, 35

Used Rydberg-atom graphs to encode multiplication tables

Discussed scalability limitations of the approach

Abstract

The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum computing algorithms to address this problem. This study introduces a quantum approach that utilizes Rydberg atoms to tackle the factorization problem. Experimental demonstrations are conducted for the factorization of small composite numbers such as $6 = 2 \times 3$, $15 = 3 \times 5$, and $35 = 5 \times 7$. This approach involves employing Rydberg-atom graphs to algorithmically program binary multiplication tables, yielding many-body ground states that represent superpositions of factoring solutions. Subsequently, these states are probed using quantum adiabatic computing. Limitations of this method are discussed, specifically addressing the scalability of current Rydberg quantum computing for the intricate computational problem.