Study Highlights Significant Gap Between Current Quantum Hardware and Shor’s Algorithm Requirements

Global: Practical Challenges in Executing Shor’s Algorithm on Existing Quantum Platforms

Researchers from six institutions, including Paul Bagourd, Julian Jang‑Jaccard, and colleagues, submitted a paper on December 17 2025 and released a revised version on January 13 2026 that investigates how today’s cloud‑accessible quantum processors perform when tasked with factoring integers using Shor’s algorithm. The study aims to determine realistic key sizes that could be compromised with existing hardware.

Background

Quantum computers are widely recognized as a potential threat to public‑key cryptosystems such as RSA and elliptic‑curve cryptography because Shor’s algorithm can factor large integers efficiently, undermining the mathematical foundations of these schemes.

Theoretical Resource Estimates

Prior theoretical analyses suggest that breaking a 2048‑bit RSA key would require fewer than one million noisy qubits when employing error‑corrected implementations of Shor’s algorithm. These estimates serve as a benchmark for evaluating the capabilities of contemporary quantum devices.

Experimental Methodology

The authors conducted empirical tests on several cloud‑based quantum computers, leveraging publicly available, open‑source implementations of Shor’s algorithm. Each experiment targeted modestly sized composite numbers to assess how hardware constraints affect algorithmic performance.

Key Findings

Results reveal a pronounced disparity between current hardware and the resources needed for cryptographically relevant factorization. Circuit constructions had to be highly customized for each modulus, indicating a lack of general‑purpose scalability. Additionally, the machines exhibited unstable fidelities, with error rates that were both high and fluctuating across runs.

Implications for Cryptography

Given the observed performance limitations, the study concludes that existing quantum platforms are far from being capable of threatening widely deployed RSA or ECC keys. Consequently, the immediate risk to current cryptographic infrastructure remains low, though the trajectory of hardware improvements warrants continued monitoring.

Future Outlook

The authors recommend further research into error‑mitigation techniques, more robust circuit designs, and systematic benchmarking across a broader set of quantum devices. Such efforts could narrow the gap and provide clearer timelines for when quantum‑based attacks might become feasible.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.