# Perfect state transfer in products and covers of graphs

@article{Coutinho2015PerfectST, title={Perfect state transfer in products and covers of graphs}, author={Gabriel Coutinho and Chris D. Godsil}, journal={Linear and Multilinear Algebra}, year={2015}, volume={64}, pages={235 - 246} }

A continuous-time quantum walk on a graph is represented by the complex matrix , where is the adjacency matrix of and is a non-negative time. If the graph models a network of interacting qubits, transfer of state among such qubits throughout time can be formalized as the action of the continuous-time quantum walk operator in the characteristic vectors of the vertices. Here, we are concerned with the problem of determining which graphs admit a perfect transfer of state. More specifically, we… Expand

#### 20 Citations

Discrete Quantum Walks on Graphs and Digraphs

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This thesis studies various models of discrete quantum walks on graphs and digraphs via a spectral approach. A discrete quantum walk on a digraph X is determined by a unitary matrix U , which acts on… Expand

Perfect quantum state transfer using Hadamard diagonalizable graphs

- Mathematics, Physics
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Abstract Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. Here, we focus on the… Expand

Quantum state transfer on Q-graphs

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- 2021

We study the existence of quantum state transfer in Q-graphs in this paper. The Qgraph of a graph G, denoted by Q(G), is the graph derived from G by plugging a new vertex to each edge of G and… Expand

Perfect state transfer on Cayley graphs over dihedral groups

- Mathematics
- 2019

Recently, there are extensive studies on perfect state transfer on graphs due to their significant applications in quantum information processing and quantum computations. However, most of the graphs… Expand

Quantum state transfer on a class of circulant graphs

- Mathematics
- Linear and Multilinear Algebra
- 2019

ABSTRACT We study the existence of quantum state transfer on non-integral circulant graphs. We find that continuous-time quantum walks on quantum networks based on certain circulant graphs with… Expand

An infinite family of circulant graphs with perfect state transfer in discrete quantum walks

- Mathematics, Computer Science
- Quantum Inf. Process.
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An infinite family of $4$-regular circulant graphs that admit perfect state transfer is constructed, the only known infinite families of examples were variants of cycles and diamond chains. Expand

Combinatorial and algebraic aspects of quantum state transfer

- Mathematics
- 2019

Reliably transferring a quantum state from one location to another, as well as generating entangled states, are important tasks to achieve in quantum spin systems. The fidelity or probability of… Expand

Continuous-time quantum walks on dynamic graphs

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- 2019

Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the… Expand

The signless Laplacian state transfer in Q-graph

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- 2021

The Q-graph of a graph G, denoted by Q(G), is the graph derived from G by plugging a new vertex to each edge of G and adding a new edge between two new vertices which lie on adjacent edges of G. In… Expand

Perfect state transfer in unitary Cayley graphs and gcd-graphs

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- 2019

Abstract In this work, we consider the problem on the existence of perfect state transfer in unitary Cayley graphs and gcd-graphs over finite commutative rings. We characterize all finite commutative… Expand

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