Transport Efficiency of Quantum Stochastic Walks on Complex Networks

In this work I examine complex networks of two-level quantum systems regarding their efficiency to transport excitons through the network. Our model uses the so-called Quantum Stochastic Walk (QSW), a version of a quantum master equation in Lindblad form (LME) which allows to parametrize the classical-quantummechanical crossover. To quantify transport efficiency several approaches can be made, as a definition is strongly dependent on the specific problem. The one used in this work is the long-time limit of a circular probability current induced by an incoherent coupling of an external node to two "ends" of the network acting as a source to an entrance node and a trap to an exit node. These links are directed and their effect is realized with additional Lindblad operators in the dissipative term of the LME. Comparing stationary solutions of node populations sheds light on the probability current through the network. In addition to the topology of the network, several parameters varied include the internal coupling constant, entrance and exit node and most notably the ratio of coherent and decoherent transitions. Network topologies studied include combs as an simple extension of the linear chain and networks constructed via a self-similar algorithm like the Vicsek graph and a glued double Cayley tree.

For sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of Stable Chaos.

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