Quantum Walks on Arbitrary Spatial Networks with Rydberg Atoms

TL;DR

This paper proposes a method to implement quantum walks on spatial networks using Rydberg atoms, enabling efficient graph-based quantum algorithms with potential quadratic speedup in spatial search tasks.

Contribution

It introduces a general approach for staggered quantum walks with Rydberg atoms on spatial networks and an efficient tessellation construction algorithm.

Findings

Achieves quadratic speedup in spatial search algorithms

Provides a scalable and reconfigurable platform for quantum walks

Demonstrates the feasibility of quantum walks on complex networks

Abstract

Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms include scalability, reconfigurable connectivity, and native multi-qubit gates, making them particularly well-suited for addressing complex network problems. These problems can often be framed as graph-based tasks, which can be efficiently addressed using quantum walks. In this work, we propose a general implementation of staggered quantum walks with Rydberg atoms, with a particular focus on spatial networks. We also present an efficient algorithm for constructing the tessellations required for the staggered quantum walk. Finally, we demonstrate that our proposal achieves quadratic speedup in spatial search algorithms.