Control by quantum dynamics on graphs

TL;DR

This paper investigates the controllability of closed quantum systems modeled by graph adjacency matrices, identifying graph structures that enable universal quantum control and linking these to quantum walks for computation.

Contribution

It introduces a novel graph-theoretic property related to cycle disarray that characterizes controllability in quantum systems.

Findings

Identifies a large family of graphs that ensure controllability.

Connects graph properties to quantum walk-based universal computation.

Provides a characterization based on cycle structure disarray.

Abstract

We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a novel graph-theoretic feature consisting of a particularly disordered cycle structure. Disregarding efficiency of control functions, but choosing subfamilies of sparse graphs, the results translate into continuous-time quantum walks for universal computation.