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

TL;DR

This paper investigates the practical limitations of executing Shor's algorithm on current quantum computers, highlighting the gap between theoretical potential and real-world hardware capabilities for factoring cryptographically relevant integers.

Contribution

It provides an experimental analysis of Shor's algorithm on existing quantum hardware, emphasizing the challenges and instability in current quantum computing platforms.

Findings

Current quantum hardware cannot reliably factor cryptographically relevant integers.

Circuit constructions require high specificity for each modulus.

Quantum machine fidelities are unstable with high and fluctuating error rates.

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.