Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction

TL;DR

This paper introduces a novel discrete-time Rydberg quantum walk implementation in multi-dimensional space, enabling simulation of various topological insulators with potential applications in quantum search algorithms.

Contribution

It presents the first discrete-time Rydberg quantum walk setup using distance-selective interactions, capable of simulating different classes of topological insulators.

Findings

Coherent quantum walks over hundreds of sites and steps are feasible with current technology.

The setup allows for designing topologically ordered boundary conditions.

Potential to enhance quantum search algorithms and simulate diverse topological phases.

Abstract

This article proposes the first discrete-time implementation of Rydberg quantum walk in multi-dimensional spatial space that could ideally simulate different classes of topological insulators. Using distance-selective exchange-interaction between Rydberg excited atoms in an atomic array with dual lattice-constants, the new setup operates both coined and coin-less models of discrete-time quantum walk (DTQW). Here, complicated coupling tessellations are performed by a global laser that exclusively excites the site at the anti-blockade region. The long-range interaction provides a new feature of designing different topologically ordered periodic boundary conditions. Limiting the Rydberg population to two excitations, coherent QW over hundreds of lattice sites and steps are achievable with the current technology. These features would improve the performance of this quantum machine in running the quantum search algorithm over topologically ordered databases as well as diversifying the range of topological insulators that could be simulated.