Measuring quantum geometric tensor of non-Abelian system in superconducting circuits

TL;DR

This paper demonstrates a method to measure the quantum geometric tensor in a non-Abelian system using superconducting circuits, revealing topological properties through quantum simulation.

Contribution

It introduces a protocol for quantum simulation of non-Abelian topological systems and measures the quantum geometric tensor in a superconducting qubit setup.

Findings

Successfully simulated the Bernevig-Hughes-Zhang model

Measured the quantum geometric tensor via interference oscillation

Extracted topological invariants to reveal topological features

Abstract

Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal interesting topological properties in non-Abelian systems, which have not been realized in practice. Here, we use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. By manipulating the Hamiltonian with periodic drivings, we simulate the Bernevig-Hughes-Zhang model and obtain the quantum geometric tensor from interference oscillation. In addition, we reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.