Quantum transport efficiency in noisy random-removal and small-world networks

Abstract

We report the results of an in-depth study of the role of graph topology on quantum transport efficiency in random removal and Watts-Strogatz networks. By using four different environmental models -noiseless, driving by classical random telegraph noise (RTN), thermal quantum bath, and bath+RTN -we compare the role of the environment and of the change in network topology in determining the quantum transport efficiency. We find that small and specific changes in network topology is more effective in causing large change in efficiency compared to that achievable by environmental manipulations for both network classes. Furthermore, we have found that noise dependence of transport efficiency in these networks can be categorized into six classes. In general, our results highlight the interplay that network topology and environment models play in quantum transport, and pave the way for transport studies for networks of increasing size and complexity -when going beyond so far often used few-site transport systems.

Perturbed graphs achieve unit transport efficiency without environmental noise

“…In a complete graph it is known that removing the edge between the vertex where the walker is initially localized and the trap leads to unit transport efficiency [41,49]. The role of removing more than one randomly picked edges from a complete graph has been investigated in [50], in both the noiseless and noisy case, showing that the maximum efficiency attainable is obtained when the network topology is modified by severing the edge between the source and the sink. On the other hand, appending a complex phase to an edge of the graph breaks the timereversal symmetry of the unitary dynamics of a CTQW and results in a continuous-time chiral quantum walk.…”