Meta-Fault-Tolerant Quantum Framework: Subsuming NISQ Limitations via Universal Rough Operator Algebra (UROA)

Abstract

The classical Quantum Error Correction (QEC) framework inherently limits logical scale up due to the macroscopic physical qubit overhead strictly required by surface codes [2] and qLDPC architectures [3]. We deductively elevate this limitation by profoundly embedding the subordinate error-correction loop into the 8-Dimensional Seonggil Matrix Space. By reinterpreting quantum decoherence not as random noise, but as a non-commutative kinetic cascade, the Topological Fractal Brake algebraically halts error propagation. This reduces logical overhead requirements to an unprecedented logarithmic scale, rigorously guaranteeingdeep-circuit coherence far beyond standard classical threshold bounds.