Scalability and Error Management in High-Qubit-Count Quantum Computing: Surface Codes, Topological Materials, and Hybrid Algorithmic Approaches

Scalability and Error Management in High-Qubit-Count Quantum Computing: Surface Codes, Topological Materials, and Hybrid Algorithmic Approaches Mehmet Keçeci ORCID : https://orcid.org/0000-0001-9937-9839 Received: 31.05.2025 “Article 6 of the series” Abstract: Quantum computers promise a revolution in science and technology by potentially solving complex problems that are intractable for classical approaches. However, realising this potential fully hinges on overcoming fundamental challenges, notably the scalability of systems with high qubit counts and the effective management of errors inherent to quantum systems. This work (Scalability and Error Management in High-Qubit-Count Quantum Computing [Unpublished pre-doctoral VI. technical reports]. Gebze Technical University, Kocaeli, Türkiye [314, 464, 470, 471]) addresses the issues of scalability and error management in high-qubit-count quantum computing systems, providing an in-depth investigation of three key solution pillars: surface codes, topological materials, and hybrid algorithmic approaches. Surface codes represent a prominent topological approach within quantum error correction (QEC) strategies, aiming to generate fault-tolerant logical qubits from physical qubits. Within this framework, the efficiency of decoding algorithms—such as BlossomV, the Minimum-Weight Perfect Matching (MWPM) algorithm, and the Union-Find algorithm—is critical for resolving error syndromes in systems scaling to millions of qubits. Our study analyses the performance of these decoders, specifically their computational wall time and the data volume generated, across varying qubit counts and error models. A second promising avenue for enhancing scalability and error management lies in the use of topological materials, such as Majorana Zero Modes (MZMs) and Weyl Semimetals (WSMs). These materials offer platforms for qubits that are intrinsically less susceptible to noise and can maintain quantum coherence for longer durations. This inherent robustness could potentially enable qubit platforms that require less complex—or even no—active error correction mechanisms. In particular, the charged and massless nature of Weyl fermions may facilitate the creation of more stable qubits by mitigating issues such as charge dispersion. Finally, recognising that no single algorithm is optimal for all problem types and noise regimes, we propose hybrid algorithmic approaches and an "Algorithm Pool" concept. This strategy involves the integration of error mitigation techniques like Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC), alongside the use of fast classical algorithms, such as Coppersmith-Winograd for matrix multiplication, to accelerate computationally intensive sub-tasks like surface code decoding. AI-driven real-time algorithm selection could further enhance the efficiency of these hybrid systems. This integrated methodology aims to simultaneously reduce computational wall time and minimise error rates at high qubit counts, thereby paving the way for fault-tolerant and scalable quantum computation. Keywords: Quantum Computing, Scalability, Error Management, Surface Codes, Topological Materials, Weyl Semimetals, Majorana Fermions, Hybrid Algorithms, Quantum Error Correction. Note: Citations and numbering are in continuation of the previous articles.