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- Title
A graph theoretical approach to states and unitary operations.
- Authors
Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish
- 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 $$C_\mathrm{NOT}$$ gate, resulting in a graphical description of Bell state generation.
- Subjects
QUANTUM states; UNITARY operators; QUANTUM operators; LAPLACIAN matrices; UNITARY transformations
- Publication
Quantum Information Processing, 2016, Vol 15, Issue 5, p2193
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-016-1250-y