TY - JOUR
T1 - Degree distribution in quantum walks on complex networks
AU - Faccin, Mauro
AU - Johnson, Tomi
AU - Biamonte, Jacob
AU - Kais, Sabre
AU - Migdal, Piotr
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014
Y1 - 2014
N2 - In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long-time probability distribution for the location of a unitary quantum walker to that of a corresponding classical walker. The distribution of the classical walker is proportional to the distribution of degrees, which measures the connectivity of the network nodes and underlies many methods for analyzing classical networks, including website ranking. The quantum distribution becomes exactly equal to the classical distribution when the walk has zero energy, and at higher energies, the difference, the socalled quantumness, is bounded by the energy of the initial state. We give an example for which the quantumness equals a Rényi entropy of the normalized weighted degrees, guiding us to regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate.
AB - In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long-time probability distribution for the location of a unitary quantum walker to that of a corresponding classical walker. The distribution of the classical walker is proportional to the distribution of degrees, which measures the connectivity of the network nodes and underlies many methods for analyzing classical networks, including website ranking. The quantum distribution becomes exactly equal to the classical distribution when the walk has zero energy, and at higher energies, the difference, the socalled quantumness, is bounded by the energy of the initial state. We give an example for which the quantumness equals a Rényi entropy of the normalized weighted degrees, guiding us to regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate.
UR - http://www.scopus.com/inward/record.url?scp=84893547709&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84893547709&partnerID=8YFLogxK
U2 - 10.1103/PhysRevX.3.041007
DO - 10.1103/PhysRevX.3.041007
M3 - Article
AN - SCOPUS:84893547709
SN - 2160-3308
VL - 3
JO - Physical Review X
JF - Physical Review X
IS - 4
M1 - 041007
ER -