First-Principles Topological Quantum Computation via Intrinsic Quantum Media

Topological quantum computing has reached a critical juncture where progress is constrained by the ontological limitations of current material platforms. This paper argues that the prevailing paradigm, based on engineering topological phases in semiconductor-superconductor hybrids, is fundamentally epiphenomenal. These systems exhibit topological protection that is conditional and fragile, evidenced by a profound disparity between their nominal superconducting energy gaps and their much smaller effective topological gaps. We introduce the Indivisibility Criterion, a set of four necessary conditions for a first-order topological qubit, which requires that topological protection, symmetry breaking, and logical operations emerge as co-constitutive, intrinsic properties of a single quantum medium. We reject hybrid platforms for failing this criterion and instead analyze three promising classes of intrinsic quantum media: chiral spin-triplet superconductors (e.g., UTe₂), Kitaev quantum spin liquids (e.g., α-RuCl₃), and fractional Chern insulators in moiré materials. We propose a validation framework based not on conventional benchmarking but on ontological verification, including tests for gap persistence under decoupling and topological invariant tomography. This work reframes the central challenge of the field from one of better engineering to one of materials discovery, advocating for a paradigm shift toward systems where fault-tolerant quantum computation is an emergent, first-principles feature of quantum matter.