Stratum Model-Based Analysis of Topological Insulators Hosting Weyl and Majorana Fermions

The development of quantum computers represents one of the most exciting and challenging endeavours in modern science. Progress in this field, particularly with the advent of the second quantum revolution, necessitates a profound interplay between diverse disciplines such as materials science, condensed matter physics, and quantum information theory. The primary aim of this work is to explore the potential of layered quantum structures containing exotic particles—Weyl and Majorana fermions—to address decoherence and noise, which are among the most significant obstacles to quantum computation. These fermions, originating from Particle Physics and emerging as quasiparticles in Condensed Matter Physics systems, offer promise for fault-tolerant qubits due to their anticipated topological protection. However, future quantum computer architectures will likely be complex, multilayered structures integrating different qubit types, various material platforms, and heterogeneous integration strategies. Classical 1, 2, or 3-dimensional approaches are insufficient for the analysis and design of such systems. In response to this need, this study proposes an original dimensional analysis framework, the "Stratum Model," inspired by the "stratum" (layer) concept from mathematical singularity theory [261–263]. In this model, each functional or physical layer constituting a quantum architecture (for example, a layer of a specific qubit type, a control electronics layer, a physical layer in a heterostructure composed of different materials, or a topologically distinct region) is defined as a "stratum" with its unique properties and degrees of freedom. Using a notation such as "Dspatial + S1 + S2 + ...", the effective spatial dimension of the system (Dspatial) can be expressed in an integrated manner along with additional "stratum" properties (Si) like the number of layers, qubit type diversity, degree of homogeneity, connectivity, topological features, and even manufacturing defects. This "Stratum Model" provides a powerful tool, particularly for the analysis of layered structures hosting Weyl and Majorana fermions or supporting their interactions. The model allows us to investigate how these exotic fermions might emerge at interfaces between different material layers (for example, superconductors, topological insulators, semimetals), how interactions between these "strata" can influence the topological properties of the fermions, and how these properties can be optimized for fault-tolerant quantum information processing. Furthermore, it aids in the identification of "defective strata" that may arise in the system over time or due to fabrication errors (for example, regions that have lost homogeneity or whose topological protection has weakened) and helps develop strategies to minimize their adverse effects on overall system performance by topologically isolating them. This bears a conceptual parallel to the management of defective regions in singularity theory [265]. Diverse physical phenomena, such as the behaviour of Dirac and Weyl semimetals under different gauge fields [266] or higher-dimensional analyses of fermions [267], can also be evaluated by assigning them to appropriate "strata" within this model. In conclusion, this work presents a novel perspective for the design, analysis, and optimization of layered quantum structures containing Weyl and Majorana fermions by employing the "Stratum Model." This approach aims to deepen our understanding of the role these exotic particles play in the advancement of quantum computers and to help pave the way for future fault-tolerant, scalable quantum architectures. This will be a significant step in translating fundamental discoveries in condensed matter physics into practical applications for quantum information processing.