Thermodynamic formalism for dissipative quantum walks

TL;DR

This paper develops a thermodynamic framework for analyzing dissipative quantum walks on directed graphs, identifying dynamical phase transitions and proposing a quantum version of PageRank for importance ranking.

Contribution

It introduces a thermodynamic formalism for dissipative quantum walks and generalizes PageRank to the quantum domain, revealing dynamical transitions.

Findings

Identification of dynamical phase transitions using large-deviation theory

Proposal of a quantum PageRank for node importance ranking

Characterization of the transition from classical to quantum walks

Abstract

We consider the dynamical properties of dissipative continuous-time quantum walks on directed graphs. Using a large-deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify transitions between dynamical regimes. For a particular class of dissipative quantum walks we propose a quantum generalization of the the classical PageRank vector, used to rank the importance of nodes in a directed graph. We also provide an example where one can characterize the dynamical transition from an effective classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct dynamical regimes.