Perturbed graphs achieve unit transport efficiency without environmental noise

TL;DR

This paper demonstrates that minimal perturbations to highly symmetric graphs can enable perfect, noise-free quantum transport efficiency, challenging the belief that environmental noise is necessary for optimal excitation transfer.

Contribution

It analytically shows that slight modifications to graph weights can break symmetries and achieve unit transport efficiency without environmental noise.

Findings

Adding weights to edges breaks symmetry and enhances transport.

Perturbations can lead to perfect transport efficiency.

Conditions for null transport efficiency are also discussed.

Abstract

Coherent transport of an excitation through a network corresponds to continuous-time quantum walk on a graph, and the transport properties of the system may be radically different depending on the graph and on the initial state. The transport efficiency, i.e., the integrated probability of trapping at a certain vertex, is a measure of the success rate of the transfer process. Purely coherent quantum transport is known to be less efficient than the observed excitation transport, e.g., in biological systems, and there is evidence that environmental noise is indeed crucial for excitation transport. At variance with this picture, we here address purely coherent transport on highly symmetric graphs, and show analytically that it is possible to enhance the transport efficiency without environmental noise, i.e., using only a minimal perturbation of the graph. In particular, we show that adding an extra weight to one or two edges, depending on whether the initial state is localized or in a superposition of two vertex states, breaks the inherent symmetries of the graph and may be sufficient to achieve unit transport efficiency. We also briefly discuss the conditions to obtain a null transport efficiency, i.e., to avoid trapping.