Topological Quantum Error Correction: A Comprehensive Review of Surface Codes, Color Codes, and Their Applications in Fault-Tolerant Quantum Computing

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.