Practical Challenges in Executing Shor's Algorithm on Existing Quantum Platforms

2025-12-17

AI Summary

This study systematically evaluates the practical capability and bottlenecks of current cloud-based quantum hardware (IBM, Rigetti) in executing Shor’s algorithm to break RSA keys. Addressing realistic scenarios such as 2048-bit RSA, we employ an open-source Shor implementation, circuit compilation optimizations, gate-level error characterization, and multi-round benchmarking. Our analysis quantifies— for the first time—the three dominant limiting factors: hardware noise, modulus-specific circuit design requirements, and dynamically varying error rates. Results show that state-of-the-art devices reliably factor integers ≤21 bits; single-qubit gate fidelities fluctuate by ±12%; each modulus necessitates manual circuit redesign; and the million-scale fault-tolerant qubits required for RSA-2048 remain orders of magnitude beyond current capabilities. The core contribution lies in identifying “circuit customizability” and “error dynamism” as critical, unresolved challenges impeding the cryptographic deployment of Shor’s algorithm.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Algorithm Configuration
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• Investigating Shor's algorithm on current quantum platforms
• Assessing practical feasibility of factoring cryptographically relevant integers
• Identifying hardware and circuit challenges in real-world execution

Innovation

• Experimentally test Shor's algorithm on cloud quantum computers
• Reveal gap between current hardware and cryptographic requirements
• Highlight need for modulus-specific circuits and stable fidelities