  Building upon our previous work, on graphical representation of a quantum
state by signless Laplacian matrix, we pose the following question. If a local
unitary operation is applied to a quantum state, represented by a signless
Laplacian matrix, what would be the corresponding graph and how does one
implement local unitary transformations graphically? We answer this question by
developing the notion of local unitary equivalent graphs. We illustrate our
method by a few, well known, local unitary transformations implemented by
single-qubit Pauli and Hadamard gates. We also show how graph switching can be
used to implement the action of the CNOT gate, resulting in a graphical
description of Bell state generation.
