A bstract We systematically explore the construction of Nielsen’s circuit complexity to a non-Lorentzian field theory keeping in mind its connection with flat holography. consider 2 d boundary dual 3 asymptotically spacetimes infinite-dimensional BMS as asymptotic symmetry algebra. compute functional two distinct ways. For Virasoro group, resembles geometric action on co-adjoint orbit. Using li...

Turing machine space complexity is related to circuit depth complexity. The relationship complements the known connection between Turing machine time and circuit size, thus enabling us to expose the related nature of some important open problems concerning Turing machine and circuit complexity. We are also able to show some connection between Turing machine complexity and arithmetic complexity.

Recently, the notion of circuit complexity defined in symmetry group manifolds has been related to geometric actions which generally arise coadjoint orbit method representation theory and play an important role quantization. On other hand, it is known that there exists a precise relation between Berry phases representations. Motivated by these connections, we elaborate on theoretic phase. As si...