Quantum Error Correction with Surface Code Analysis on Quantum Computing platform

N Raji

Quantum error correction (QEC) represents a critical enabler for fault-tolerant quantum computing, protecting fragile quantum states from decoherence and operational errors. This paper provides a comprehensive analysis of leading quantum error correction schemes, focusing on surface codes and topological codes within the context of Noisy Intermediate-Scale Quantum (NISQ) era processors. We examine the theoretical foundations of stabilizer codes, compare surface code implementations with code distances ranging from d=3 to d=17, and analyze topological codes including toric codes and color codes. Our investigation encompasses syndrome extraction circuits, logical qubit encoding strategies, and threshold analysis for contemporary quantum hardware platforms. Performance metrics reveal that surface codes achieve error thresholds of approximately 1% with realistic noise models, while topological codes offer architectural advantages for specific qubit connectivity constraints. We discuss implementation challenges on current NISQ processors including IBM Quantum, Google Sycamore, and IonQ systems, addressing qubit overhead, gate fidelity requirements, and decoding algorithms. This analysis provides insights for selecting appropriate error correction schemes based on application requirements and hardware capabilities.

Christian Kraglund Andersen, Ants Remm, Stefania Lazar +6 more

Christian Kraglund Andersen, Ants Remm, Stefania Lazar +6 more

Rohan Timmaraju

Quantum Computing is a computing framework that takes advantage of unique quantum mechanical properties (such as superposition and entanglement) to perform calculations and implement algorithms that could offer exponential speed-ups over classical computing. However, in physical implementations of such quantum computers, qubits – the fundamental components of these systems – can accumulate errors that must be accounted for. In order to mitigate these errors, various quantum error correction (QEC) codes have been developed, including the repetition code and surface codes. In this experiment I implement and evaluate three types of QEC codes on the Qiskit simulator to compare their efficacy and applicability in correcting for different kinds of errors. I hypothesize that surface codes, with their more effective design and range of correction methods, should perform the best with much lower error thresholds and resultant logical error rates. The results support the hypothesis and suggest that surface codes are a viable method of implementing scalable error correction in quantum computers.

Google Quantum AI, Lee, Joonho

Proof

Mirza Adnan Mohtashim

Topological Quantum Error Correction: A Comprehensive Review of Surface Codes, Color Codes, and Their Applications in Fault-Tolerant Quantum Computing (2026) by Mirza Adnan Mohtashim is a technically rigorous review of topological quantum error correction (QEC). It examines the stabilizer formalism, surface and color codes (with anyonic braiding and geometric interpretations of Knill-Laflamme conditions), lattice surgery, decoding algorithms (including Clifford GNNs), magic state distillation, 3D codes, self-correction via the Peierls argument, and hardware implementations across superconducting (Google below-threshold d=17, IBM heavy-hex), trapped-ion, and neutral-atom platforms up to 2026. The work includes novel geometric perspectives on noise and unified anyonic views, serving as a key reference for fault-tolerant quantum computing research.