Simulating dynamical quantum Hall effect with superconducting qubits

TL;DR

This paper proposes an experimental scheme using superconducting qubits to simulate the dynamical quantum Hall effect and observe interaction-induced topological transitions through Berry curvature measurements.

Contribution

It introduces a method to realize a 1D Heisenberg model with superconducting qubits and demonstrates how to observe topological transitions via Berry curvature in small qubit arrays.

Findings

Quantized plateaus in Berry curvature indicate the dynamical quantum Hall effect.

Topological transitions are observable even in a two-qubit system.

Practical experimental conditions for observing the effect are analyzed.

Abstract

We propose an experimental scheme to simulate the dynamical quantum Hall effect and the related interaction-induced topological transition with a superconducting-qubit array. We show that a one-dimensional Heisenberg model with tunable parameters can be realized in an array of superconducting qubits. The quantized plateaus, which is a feature of the dynamical quantum Hall effect, will emerge in the Berry curvature of the superconducting qubits as a function of the coupling strength between nearest neighbor qubits. We numerically calculate the Berry curvatures of two-, four- and six-qubit arrays, and find that the interaction-induced topological transition can be easily observed with the simplest two-qubit array. Furthermore, we analyze some practical conditions in typical experiments for observing such dynamical quantum Hall effect.