Staggered quantum walks with superconducting microwave resonators

TL;DR

This paper proposes implementing the staggered quantum walk model using superconducting microwave resonators, enabling tunable local operations and potential applications in quantum information processing.

Contribution

It introduces a practical implementation method for staggered quantum walks with superconducting resonators, bridging theoretical models and experimental realization.

Findings

Implementation feasibility with superconducting resonators

Tunable interactions enable flexible quantum walk dynamics

Potential extension to complex graph structures

Abstract

The staggered quantum walk model on a graph is defined by an evolution operator that is the product of local operators related to two or more independent graph tessellations. A graph tessellation is a partition of the set of nodes that respects the neighborhood relation. Flip-flop coined quantum walks with the Hadamard or Grover coins can be expressed as staggered quantum walks by converting the coin degree of freedom into extra nodes in the graph. We propose an implementation of the staggered model with superconducting microwave resonators, where the required local operations are provided by the nearest neighbor interaction of the resonators coupled through superconducting quantum interference devices. The tunability of the interactions makes this system an excellent toolbox for this class of quantum walks. We focus on the one-dimensional case and discuss its generalization to a more general class known as triangle-free graphs.