A bstract In the geometric approach to defining complexity, operator complexity is defined as distance in space. this paper, based on analogy with circuit size adopted metric of space where path length complexity. The typical sectional curvatures geometry are positive. It further proved that always positive if an arbitrary function size, while usually expected be negatively curved manifolds. By...

Abstract Topological spaces have numerous applications for quantum matter with protected chiral edge modes related to an integer-valued Chern number, which also characterizes the global response of a spin-1/2 particle magnetic field. Such models can describe topological Bloch bands in lattice Hamiltonians. Here we introduce interactions system spin-1/2s reveal class states rational-valued numbe...