Executive Summary
The development of a large-scale, fault-tolerant quantum computer is a paramount challenge in modern science. Its primary obstacle is quantum decoherence, where the fragile states of conventional qubits collapse due to environmental noise. This fragility requires extensive and resource-heavy quantum error correction (QEC) to manage. As a revolutionary alternative, topological quantum computing proposes to solve this problem at the hardware level. It encodes quantum information in the global, non-local properties of a system, rendering it intrinsically immune to local disturbances.
This approach is centered on creating and manipulating exotic quasiparticles called non-Abelian anyons, with Majorana zero modes (MZMs) being the leading candidate. This report first examines the foundational principles of topological protection. It then surveys the primary experimental platforms being pursued, from semiconductor-superconductor hybrids to fractional quantum Hall systems. From there, the report delves into the contentious experimental quest to definitively prove the existence of MZMs. It analyzes the history of promising but ambiguous signatures, such as the zero-bias conductance peak (ZBCP), and dissects recent controversies surrounding high-profile experimental claims, retractions, and the fierce debate over verification methods like the Topological Gap Protocol (TGP).
Looking forward, the report outlines the necessary next steps for the field. These steps are centered on next-generation experiments that can unambiguously demonstrate non-Abelian braiding statistics. Finally, we provide a comparative analysis against more mature qubit technologies. We conclude that while the topological approach faces profound fundamental science challenges and remains a high-risk, long-term endeavor, its potential to dramatically reduce QEC overhead and its role in advancing materials science make it a critical and compelling frontier in the future of computing.
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