We consider how continuous-time quantum walks can be used for graph matching. We focus in detail on both exact and inexact graph matching, and consider in depth the problem of measuring graph similarity. We com
We consider two graph invariants inspired by quantum walks- one in continuous time and one in discrete time. We will associate a matrix algebra called a cellular algebra with every graph. We show that, if the cellular algebras of two graphs have a similar structure, then they are not ...
Measuring graph similarity through continuous-time quantum walks and the quantum jensen-shannon divergence. Physical Review E 91, 022815.Rossi, L., Torsello, A., Hancock, E.R.: Measuring graph similarity through continuous- time quantum walks and the quantum jensen-shannon divergence. Physical ...
One way to introduce directional bias is via time-reversal symmetry breaking that can be achieved with chiral quantum walks, where complex phases are added to the edge weights. However, it is not known for which complex phases values and on which graphs quantum transport can be enhanced. ...
Interpolated quantum walksWe solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set consists of a single vertex, the number of steps of the quantum walk is quadratically smaller than the classical ...
Quantum PhysicsWe clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new class of coined quantum walk by a ...
We address continuous-time quantum walks on graphs, and discuss whether and how quantum-limited measurements on the walker may extract information on the tunnelling amplitude between the nodes of the graphs. For a few remarkable families of graphs, we evaluate the ultimate quantum bound to ...
We consider two graph invariants inspired by quantum walks鈥攐ne in continuous time [John King Gamble, Mark Friesen, Dong Zhou, Robert Joynt, and S. N. Coppersmith. Two-particle quantum walks applied to the graph isomorphism problem. Phys. Rev. A, (81), May 2010] and one in discrete ...
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix quantum walk model, the number of edges is ...
and Fedichkin, L. (2006) Continuous-Time Quantum Walks on a Cycle Graph. Physical Review A, 73, Ar- ticle ID: 012313. http://dx.doi.org/10.1103/PhysRevA.73.012313Dmitry Solenov and Leonid Fedichkin, Continuous-Time Quantum Walks on a Cycle Graph, Phys. Rev. A 73, 012313 (2006)....