  We describe a cohomological framework for measurement based quantum
computation, in which symmetry plays a central role. Therein, the essential
information about the computational output is contained in topological
invariants, namely elements of two cohomology groups. One of those invariants
applies to the deterministic case, and the other to the general probabilistic
case. The same invariants also witness quantumness in the form of
contextuality. In result, they give rise to fundamental algebraic structures
underlying quantum computation.
