# A graph theoretical approach to states and unitary operations

A graph theoretical approach to states and unitary operations 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 $$C_\mathrm{NOT}$$ C NOT gate, resulting in a graphical description of Bell state generation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# A graph theoretical approach to states and unitary operations

, Volume 15 (5) – Feb 4, 2016
20 pages

/lp/springer_journal/a-graph-theoretical-approach-to-states-and-unitary-operations-ElBscM0cjL
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1250-y
Publisher site
See Article on Publisher Site

### 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 $$C_\mathrm{NOT}$$ C NOT gate, resulting in a graphical description of Bell state generation.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 4, 2016

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