Implementation of Shor Algorithm: Factoring a 4096-Bit Integer Under Specific Constraints

TL;DR

This paper presents an improved implementation of Shor's quantum algorithm that efficiently factors a 4096-bit integer under specific constraints, demonstrating advancements in quantum algorithm practicality for large integer factorization.

Contribution

The study introduces a novel implementation of Shor's algorithm optimized for modular computation, enabling the factorization of larger integers with improved efficiency compared to existing methods.

Findings

Significant efficiency improvements over SOTA methods

Successful factorization of a 4096-bit integer

Enhanced suitability for real-world quantum applications

Abstract

In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum algorithms suitable for real-world applications has become a crucial research direction. This study focuses on the implementation of Shor algorithm, aiming to improve modular computation efficiency and demonstrate the factorization of a 4096-bit integer under specific constraints. Experimental results, when compared with state-of-the-art (SOTA) methods, indicate a significant improvement in efficiency while enabling the factorization of longer integers.