Topological QBits in Flux-Quantized Super-Gravity

TL;DR

We address flux-quantization in 11D supergravity to classify topologically stabilized C-field configurations sourced by M-branes via non-abelian cohomology and Cohomotopy. Non-perturbative quantization of the self-dual 3-form on the M5 worldvolume, constrained by dG4 = 0 and dG7 = 1/2 G4 G4, yields topologically nontrivial sectors with anyonic solitons, suggesting a first-principles holographic route to topological qubits beyond large-N limits. Topological observables on flux-quantized M5 sectors admit a braid-group action: adiabatic motion of M5-defect anyons in the transverse plane implements topological quantum gates via the mapping class group of punctured planes, realized as the action of Br_n on Obs_bullet = H_bullet( Omega Maps((R^2 minus n punctures)_compact, S^2); C). The construction connects to holographic anyons and is expressible in homotopy-type programming languages, where classifying spaces encode braid transport and gates reduce to one-liner type-transport expressions in languages like Agda or cubical Agda. Vista: cohesive homotopy theory provides a framework in which spacetime and brane content emerge from computational logic; the super-point and higher extensions generate the D=11 super-spacetime and the M-brane bouquet, with the C-field cocycle realized as a non-abelian 4-Cohomotopy structure and M2/M5 WZW terms intertwined. This synthetic emergence links topological qbits, holography, and quantum computation, suggesting a unified viewpoint in which physical processes are computations within a cohesive topos.

Abstract

We first give a brief exposition of our recent realization of anyonic quantum states on single M5-brane probes in 11D super-gravity backgrounds, by non-perturbative quantization of the topological sector of the self-dual tensor field on the 6D worldvolume, after its proper flux-quantization. This opens the prospect of holographic models for topological qbits away from the usual but unrealistic limit of large numbers of branes. At the same time, the elementary homotopy-theoretic nature of the construction yields a slick expression of topological quantum gates in homotopically-typed programming languages, opening the prospect of topological-hardware aware quantum programming. In view of these results, we end with some more meta-physical remarks on (cohesive) homotopy (type) theory in view of emergent fundamental physics and, possibly, M-theory.