A graph theoretical approach to states and unitary operations
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Publication:296156
DOI10.1007/S11128-016-1250-YzbMATH Open1338.81211arXiv1502.07821OpenAlexW3103033167MaRDI QIDQ296156
Author name not available (Why is that?)
Publication date: 14 June 2016
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1502.07821
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