scholarly journals Some classes of integral circulant graphs either allowing or not allowing perfect state transfer

2009 ◽  
Vol 22 (10) ◽  
pp. 1609-1615 ◽  
Author(s):  
Milan Bašić ◽  
Marko D. Petković
Keyword(s):  
Perfect State ◽  
Circulant Graphs ◽  
State Transfer ◽  
Perfect State Transfer

scholarly journals Perfect state transfer in integral circulant graphs

2009 ◽  
Vol 22 (7) ◽  
pp. 1117-1121 ◽  
Author(s):  
Milan Bašić ◽  
Marko D. Petković ◽  
Dragan Stevanović
Keyword(s):  
Perfect State ◽  
Circulant Graphs ◽  
State Transfer ◽  
Perfect State Transfer

scholarly journals PARAMETERS OF INTEGRAL CIRCULANT GRAPHS AND PERIODIC QUANTUM DYNAMICS

2007 ◽  
Vol 05 (03) ◽  
pp. 417-430 ◽  
Author(s):  
NITIN SAXENA ◽  
SIMONE SEVERINI ◽  
IGOR E. SHPARLINSKI
Keyword(s):  
Quantum Dynamics ◽  
Perfect State ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Odd Order ◽  
State Transfer ◽  
Network Topologies ◽  
Perfect State Transfer ◽  
Exact Bounds

The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system whose hamiltonian is identical to the adjacency matrix of a circulant graph is periodic if and only if all eigenvalues of the graph are integers (that is, the graph is integral). Motivated by this observation, we focus on relevant properties of integral circulant graphs. Specifically, we bound the number of vertices of integral circulant graphs in terms of their degree, characterize bipartiteness and give exact bounds for their diameter. Additionally, we prove that circulant graphs with odd order do not allow perfect state transfer.

Laplacian Perfect State Transfer in Extended Neighborhood Coronas

2021 ◽  
Vol 37 (12) ◽  
pp. 1921-1932
Author(s):  
Yi Peng Li ◽  
Xiao Gang Liu ◽  
Sheng Gui Zhang
Keyword(s):  
Perfect State ◽  
State Transfer ◽  
Perfect State Transfer

scholarly journals Perfect state transfer on abelian Cayley graphs

2019 ◽  
Vol 563 ◽  
pp. 331-352 ◽  
Author(s):  
Ying-Ying Tan ◽  
Keqin Feng ◽  
Xiwang Cao
Keyword(s):  
Cayley Graphs ◽  
Perfect State ◽  
State Transfer ◽  
Perfect State Transfer

scholarly journals Quantum walks on graphs of the ordered Hamming scheme and spin networks

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Hiroshi Miki ◽  
Satoshi Tsujimoto ◽  
Luc Vinet
Keyword(s):  
Magnetic Fields ◽  
Quantum Walks ◽  
Perfect State ◽  
Spin Networks ◽  
Krawtchouk Polynomials ◽  
Energy Eigenstates ◽  
State Transfer ◽  
Perfect State Transfer ◽  
Local Magnetic Fields ◽  
Basis Vectors

It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors.

scholarly journals Perfect state transfer in long-range interacting spin chains

2008 ◽  
Vol 78 (2) ◽  
Author(s):  
Giulia Gualdi ◽  
Vojtech Kostak ◽  
Irene Marzoli ◽  
Paolo Tombesi
Keyword(s):  
Long Range ◽  
Spin Chains ◽  
Perfect State ◽  
State Transfer ◽  
Perfect State Transfer
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