Recursion Optimisation and Extreme Noise Tolerance in Quantum Error Correction Algorithms: Assessing the Potential for a Quantum Leap

Mehmet Keçeci

ORCID : https://orcid.org/0000-0001-9937-9839

Received: 01.10.2025

“Article 7 of the series”

Abstract: This study (Recursion Optimisation and Extreme Noise Tolerance in Quantum Error Correction Algorithms [Unpublished pre-doctoral VII. technical reports]. Gebze Technical University, Kocaeli, Türkiye [313, 465, 472, 473]) provides an in-depth investigation into the optimisation of recursion performance in Quantum Error Correction (QEC) algorithms and their tolerance under extreme noise conditions, with the aim of developing effective strategies against noise, one of the most significant obstacles to fault-tolerant quantum computation. Although the non-Abelian statistics and topological protection properties of Majorana fermions offer promising qubit candidates for quantum computers, realising this potential is highly dependent on developing scalable and noise-resilient QEC mechanisms. Our research focuses specifically on the limitations of recursion depth encountered by algorithms such as Union-Find (UF), UF with Naive Syndromes (UFNS), and the Minimum-Weight Perfect Matching (MWPM) algorithm, which are commonly used in surface codes. To overcome these limitations, we applied recursion optimisation techniques—including Path Compression, Union by Rank, and Iterative Implementation—which achieved a significant reduction in the number of recursion calls, thereby preventing the system from reaching its recursion limits. These optimisations enabled the simulation and analysis of high-qubit-count systems, such as planar and cubic lattices. This thesis formalizes a hierarchical noise classification. We define a ‘High Noise’ scenario as a single error source with p > 0.5, and introduce a more severe ‘Extreme Noise’ regime for scenarios where at least two such high-intensity sources (p ≥ 0.8-0.9) are simultaneously active.” The performance of QEC algorithms under these challenging scenarios was evaluated in terms of error correction success rates and resource requirements. The findings indicate that, particularly for high qubit counts, the optimised versions of the Union-Find algorithm can be more efficient than MWPM within certain parameter ranges. It is concluded that inherently low-noise or noiseless systems, such as those based on Majorana Zero Modes (MZMs), possess a higher potential for enabling a paradigm-shifting advancement, defined here as a “Quantum Leap.” Although significant strides are being made with current qubit technologies and error correction methods, achieving true quantum supremacy is anticipated to require innovative approaches, such as MZM-based platforms, alongside more sophisticated QEC strategies tailored to them. This work offers concrete solutions for enhancing the practical applicability of QEC algorithms, elucidates the impact of extreme noise conditions on quantum systems, and provides critical insights for the design of future fault-tolerant quantum computers.

Keywords: Quantum Error Correction, Recursion Optimisation, Extreme Noise, Majorana Fermions, Surface Codes, Quantum Leap, Union-Find Algorithm, Fault Tolerance, Topological Quantum Computing, MWPM, UFNS.

Note: Citations and numbering are in continuation of the previous articles.