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

Seonggil Lee

Published Oct 4, 2026• 0 citations
Publisher

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.

DOI
10.5281/zenodo.23134504

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The practical implementation of Quantum Key Distribution (QKD) is heavily constrained by the PLOB bound [1], exponential optical channel loss, and device-dependent side-channel attacks [2]. We deductively elevate these limitations by structurally embedding the quantum optical channel into the 8-Dimensional Seonggil Matrix Space. By redefining decoherence and measurement disturbance as non-commutative quantum friction, the Topological Fractal Brake algebraically suppresses information leakage, bypassing classical linear bounds. This rigorously establishes a theoretical framework for a global, topologically lossless quantum internet without macroscopic repeater overhead.
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Fault-tolerant quantum computing (FTQC) is required to execute quantum algorithms capable of tackling computationally intractable problems in chemistry, material science, and cryptography. Noisy Intermediate-Scale Quantum (NISQ) devices remain constrained by physical error rates that degrade quantum coherence over short circuit depths. Quantum error correction (QEC) protects fragile logical states by encoding them into non-local degrees of freedom across topological physical qubit arrays. This research presents a comprehensive architectural and theoretical evaluation of three primary QEC paradigms: planar surface codes, topological color codes, and asymptotic quantum low-density parity-check (qLDPC) codes. We examine error thresholds, transversal gate constraints governed by the Eastin-Knill theorem, magic state distillation (MSD) overheads, lattice surgery, and classical decoding latencies across superconducting transmons, trapped ions, and neutral atom platforms.