Observing Topological Invariants Using Quantum Walk in Superconducting Circuits

TL;DR

This paper demonstrates a method to directly measure topological invariants in quantum materials using quantum walks implemented in superconducting circuits, enabling digital simulation of topological phases.

Contribution

It introduces a superconducting circuit-based quantum walk approach to measure topological invariants, with a novel interference technique for direct measurement.

Findings

Successful implementation of split-step quantum walks in superconducting circuits

Direct measurement of winding numbers associated with topological phases

Potential extension to higher-dimensional topological systems

Abstract

The direct measurement of topological invariants in both engineered and naturally occurring quantum materials is a key step in classifying quantum phases of matter. Here we motivate a toolbox based on time-dependent quantum walks as a method to digitally simulate single-particle topological band structures. Using a superconducting qubit dispersively coupled to a microwave cavity, we implement two classes of split-step quantum walks and directly measure the topological invariant (winding number) associated with each. The measurement relies upon interference between two components of a cavity Schr\"odinger cat state and highlights a novel refocusing technique which allows for the direct implementation of a digital version of Bloch oscillations. Our scheme can readily be extended to higher dimensions, whereby quantum walk-based simulations can probe topological phases ranging from the quantum spin Hall effect to the Hopf insulator.