Accuracy, Noise, and Scalability in Quantum Computation: Strategies for the NISQ Era and Beyond

Mehmet Keçeci

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

Received: 26.05.2025

“Article 3 of the series”

Abstract:

Quantum computers promise to revolutionize science and technology by offering the potential to solve complex problems intractable with classical approaches. However, realizing this potential hinges on effectively managing the noise and errors inherent in quantum systems, which threaten computational accuracy. This work (Accuracy, Noise, and Scalability in Quantum Computation [Unpublished doctoral dissertation IV. Report]. Gebze Technical University, Kocaeli, Türkiye [318, 462]) has explored a broad spectrum, from the fundamentals of quantum computation to strategies for enhancing the performance of devices in the Noisy Intermediate-Scale Quantum (NISQ) era, with a particular focus on the critical role of quantum error correction (QEC) codes and the decoder algorithms developed for them. While various methods exist for characterizing and manipulating quantum states, the scalability of these methods becomes a significant issue as the number of qubits increases. The measurement process itself also requires careful planning as it perturbs the quantum state. QEC codes, especially topological codes like surface codes, developed to overcome these challenges, form the foundation of fault-tolerant quantum computation. The success of a QEC code largely depends on the performance of its decoder algorithm, which analyses error syndromes to detect and correct the most probable errors. Alongside classical approaches like Minimum-Weight Perfect Matching (MWPM) and Union-Find, newer and potentially more powerful methods such as Maximum-Likelihood Decoders (MLD) and Neural Network-based Decoders (NNbD) are active areas of research. A prominent aspect of this study is the demonstration that, even with limited classical computing resources, the theoretical scalability of quantum error correction mechanisms can be pushed to remarkable limits using sophisticated simulation techniques and algorithmic ingenuity. Notably, striking results such as the simulation and verification of surface code error correction algorithms for systems of 25 million theoretical qubits have been achieved on a personal computer. Furthermore, the graphical visualization of error correction solutions for systems exceeding 100,000 theoretical qubits underscores the analysability of such complex systems. These findings indicate that error correction principles are theoretically applicable to very large systems and that classical simulations continue to be a valuable tool in this exploratory journey. In the future, key objectives will include the development of more efficient and scalable decoders, the discovery of new QEC codes, the creation of realistic noise models, advancements in hardware-software co-design, and the execution of complex algorithms on logical qubits. Quantum error correction will continue to play a central role on the path to fault-tolerant quantum computation, and theoretical and simulational work in this area will offer significant contributions to the realization of practical quantum computers. Large-scale simulation achievements driven by the creativity of individual researchers, as highlighted here, bolster hopes for the future of the field.

Keywords: Quantum Computing, Decoder, Simulation, Scalability, Qubit, Quantum Error Correction, QEC, Stabilizer Codes, Topological Codes, Surface Code, Fault-Tolerant Quantum Computation, Quantum Noise.

Note: Citations and numbering are in continuation of the previous article [242–244].