  In this article, we develop a graphical calculus for multi-qudit computations
with generalized Clifford algebras, using the algebraic framework we developed
in our previous paper. We build our graphical calculus out of a fixed set of
graphical primitives defined by algebraic expressions constructed out of
elements of a given generalized Clifford algebra, a graphical primitive
corresponding to the ground state, and also graphical primitives corresponding
to projections onto the ground state of each qudit. We establish many
"superpower"-like properties of the graphical calculus using purely algebraic
methods, including a novel algebraic proof of a Yang-Baxter-like equation. We
also derive several new identities for the braid elements, which are key to our
proofs. In terms of physics, we connect these braid identities to physics by
showing the presence of a conserved charge. Furthermore, we demonstrate that in
many cases, the verification of involved vector identities can be reduced to
the combinatorial application of two basic vector identities. Finally, we show
how to explicitly compute various vector states in an efficient manner using
algebraic methods.
