Ali Moradi

Graph states admit a clean graph-theoretic classification of local-Clifford equivalence: two graph states are equivalent under tensor products of single-qubit Cliffords if and only if their graphs are related by a sequence of local complementations. Graph states are themselves a special case of graph codes, in which a vertex subset selects a logical qubit encoded across the vertices of the underlying graph. We provide the analog of the local-Clifford story for the single-qubit-encoded case: an explicit graph-theoretic recipe for the action of every logical single-qubit Clifford on the graph-code descriptor and the encoded-state coefficients. Each logical Clifford is implemented at the physical level by a circuit of single-qubit Cliffords alone, with no two-qubit entangling gates. We discuss the calculus, its closure, its physical implementation, and several open directions.