Phys. Rev. A 96, 032305 (2017)

Credit: APS

Most of us are familiar with the concept of a random walk — a classic example is provided by a pollen particle suspended in water. But what if we replace the pollen with a quantum system, to produce a so-called quantum walk? Interference effects between the possible trajectories of the walker substantially modify the resulting dynamics — for example, that's what makes quantum searches so efficient.

Running a random walk over a graph (pictured) allows some of the graph's geometrical features to be probed. And it's conjectured that a quantum walker could do this even better. Unfortunately, there is a caveat: quantum systems need to satisfy unitarity, and this means that quantum walks have been limited to undirected (symmetric) graphs.

Now, Josh Izaac et al. show that this needn't be the case: by taking advantage of parity–time (PT)-symmetry, which emerges in non-Hermitian systems with gain and loss, they have demonstrated that the more general class of PT-symmetric quantum walks generates viable dynamics on directed graphs, and can be used to calculate network centrality performing as well as PageRank, the algorithm behind many of today's search engines.