Axiomatic Emergence AE; Information Topological Dynamics and Lower Bounds of Circuit Complexity: A Testable Derivation

changzheng zhou, ZIQING zhou

Published Feb 28, 2026• 0 citations

Abstract

Within the framework of axiomatic emergence, by introducing a rigorous definition of information topological charge, and starting from the axioms of information conservation (A1) and finite-step computability (A2), we strictly derive a newlower bound formula for the depth of quantum circuits. This formula relates thelower bound of circuit depth to the topological complexity of the circuit (characterized by the square of the information topological charge) and the quantum speedlimit. More importantly, the derivation process is closed, and its results directlypredict a universal, counterintuitive negative correlation between the volume-lawcoefficient of subsystem entanglement entropy and the topological complexity of itscomplementary subsystem during the evolution of random quantum circuits. Thisprediction can be tested by running specific random circuits on superconductingquantum processors and performing precise measurements, thereby providing anunprecedented quantitative experimental adjudication for this theoretical framework. Through small-scale numerical simulations, we verify the suppression effectof the entanglement entropy growth coefficient under non-zero topological chargeconditions, and the results are qualitatively consistent with the theoretical predictions.

DOI: 10.5281/zenodo.18814240

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