Correlated Decoherence and the Possible Limits of Scalable Fault-Tolerant Quantum Computing: A Symmetry-Based Perspective

Over three decades after the formulation of early quantum algorithms, the realization of large-scale, fault-tolerant quantum computers remains constrained within the Noisy Intermediate-Scale Quantum (NISQ) regime. This paper critically re-evaluates the foundational assumptions underlying the Quantum Threshold Theorem and scalable Quantum Error Correction (QEC). We contrast classical error-suppression paradigms—specifically von Neumann’s majority-logic architecture for unreliable components—with the physical realities of continuous SU(2) symmetries in Hilbert space. We argue that the physical implementation of fault-tolerant quantum computing relies on a highly idealized model of uncorrelated, local Markovian noise, whose physical realizability at macroscopic scales remains contested. By examining interaction Hamiltonians in highly entangled macroscopic states, we demonstrate that collective decoherence channels and spatial noise correlations scale nonlinearly with register size n. This correlated phase drift acts as a directional force field—analogous to a long-wavelength hydrodynamic gradient across a field of coupled oscillators—rendering spatial averaging and independent syndrome measurements mathematically incapable of distinguishing systemic logic from collective environmental shifts. Consequently, we propose that universal quantum computers should not be conceptualized as scalable digital Turing machines, but rather as highly specialized, analog physical emulators bound by fundamental physical limits of continuous symmetry preservation.