Practical Challenges in Executing Shor's Algorithm on Existing Quantum Platforms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914250224566272 |
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| author | Bagourd, Paul Jang-Jaccard, Julian Lenders, Vincent Mermoud, Alain Hoefler, Torsten Hempel, Cornelius |
| author_facet | Bagourd, Paul Jang-Jaccard, Julian Lenders, Vincent Mermoud, Alain Hoefler, Torsten Hempel, Cornelius |
| contents | Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys could be broken using Shor's algorithm with fewer than a million noisy qubits. Although such machines do not yet exist, the availability of smaller, cloud-accessible quantum processors and open-source implementations of Shor's algorithm raises the question of what key sizes can realistically be factored with today's platforms. In this work, we experimentally investigate Shor's algorithm on several cloud-based quantum computers using publicly available implementations. Our results reveal a substantial gap between the capabilities of current quantum hardware and the requirements for factoring cryptographically relevant integers. In particular, we observe that circuit constructions still need to be highly specific for each modulus, and that machine fidelities are unstable, with high and fluctuating error rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Practical Challenges in Executing Shor's Algorithm on Existing Quantum Platforms Bagourd, Paul Jang-Jaccard, Julian Lenders, Vincent Mermoud, Alain Hoefler, Torsten Hempel, Cornelius Quantum Physics Cryptography and Security Emerging Technologies Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys could be broken using Shor's algorithm with fewer than a million noisy qubits. Although such machines do not yet exist, the availability of smaller, cloud-accessible quantum processors and open-source implementations of Shor's algorithm raises the question of what key sizes can realistically be factored with today's platforms. In this work, we experimentally investigate Shor's algorithm on several cloud-based quantum computers using publicly available implementations. Our results reveal a substantial gap between the capabilities of current quantum hardware and the requirements for factoring cryptographically relevant integers. In particular, we observe that circuit constructions still need to be highly specific for each modulus, and that machine fidelities are unstable, with high and fluctuating error rates. |
| title | Practical Challenges in Executing Shor's Algorithm on Existing Quantum Platforms |
| topic | Quantum Physics Cryptography and Security Emerging Technologies |
| url | https://arxiv.org/abs/2512.15330 |