# Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains

## TL;DR

This paper demonstrates how a tunable superconducting qubit chain can realize topological phases, enabling measurement of topological invariants and entanglement-dependent topological pumping through quantum dynamics.

## Contribution

It introduces a protocol for constructing generalized SSH models in superconducting qubits and links quantum dynamics to topological invariants like winding and Chern numbers.

## Key findings

- Quantum dynamics reveal topological winding number.
- Adiabatic transfer enables entanglement-dependent topological pumping.
- Results are robust against qubit coupling imperfections.

## Abstract

We propose a protocol using a tunable Xmon qubit chain to construct generalized Su-Schrieffer-Heeger (SSH) models that support various topological phases. We study the time evolution of a single-excitation quantum state in a SSH-type qubit chain and find that such dynamics is linked to topological winding number. We also investigate the adiabatic transfer of a single-excitation quantum state in a generalized SSH-type qubit chain and show that this process can be connected with topological Chern number and be used to generate a novel entanglement-dependent topological pumping. All results have been demonstrated to be robust against qubit coupling imperfections and can be observed in a short Xmon qubit chain. Our study provides a simple method to directly measure topological invariants rooted in momentum space using quantum dynamics in real space.