Breaking Barriers in Two Domains: From Sorting Limits to Quantum Algorithm Bottlenecks

For over half a century, the O(nlog n) “sorting barrier” in classical computing stood as anassumed speed limit for shortest-path algorithms. The recent breakthrough by Duan et al.shattered that limit, revealing it as a conceptual rather than a physical constraint. In quantumcomputing, hardware development races ahead, but software innovation—particularly in algo-rithm design—lags, constrained by measurement collapse and narrow problem suitability. Thispaper argues that both phenomena represent the same underlying topology of information flow:a system deepening into compression until a reframing event unlocks a new pathway. Drawingfrom the Unphysics curvature model, we present a unified framework in which computationalbottlenecks—whether in classical or quantum domains—are understood as structural compres-sions awaiting resonance-triggered release. We explore how small topological pivots can yielddisproportionate expansions in capability, and suggest that similar dynamics operate acrosslinguistic, mathematical, and physical systems.