# Measurement of the topological Chern number by continuous probing of a qubit subject to a slowly varying Hamiltonian

## TL;DR

This paper proposes a measurement scheme using continuous monitoring and feedback to determine the topological Chern number of a qubit system with a slowly varying Hamiltonian, applicable to superconducting qubits.

## Contribution

It introduces a novel continuous probing method combined with feedback control to measure topological invariants in quantum systems.

## Key findings

- Effective measurement of Berry curvature demonstrated
- Feedback Hamiltonian compensates measurement back-action
- Applicable to superconducting qubits with microwave control

## Abstract

We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the gradient of the Hamiltonian with respect to one parameter during a quasi-adiabatic quench of the other. Measurement back-action leads to disturbance of the system dynamics, but we show that this can be compensated by a feedback Hamiltonian. As an example, we analyze the implementation with a superconducting qubit subject to time varying, near resonant microwave fields; equivalent to a spin 1/2 particle in a magnetic field.