# A gradient algorithm for Hamiltonian identification of open quantum systems

## TL;DR

This paper introduces a gradient-based algorithm for identifying unknown parameters in open quantum systems using measurement data, applicable to both Markovian and non-Markovian environments, demonstrated on circuit QED systems.

## Contribution

A novel gradient algorithm for Hamiltonian identification in open quantum systems, including non-Markovian environments, with validation on circuit QED models.

## Key findings

- Effective in identifying Hamiltonians in Markovian systems
- Capable of learning spectra of non-Markovian environments
- Validated on circuit QED systems with promising results

## Abstract

In this paper, we present a gradient algorithm for identifying unknown parameters in an open quantum system from the measurements of time traces of local observables. The open system dynamics is described by a general Markovian master equation based on which the Hamiltonian identification problem can be formulated as minimizing the distance between the real time traces of the observables and those predicted by the master equation. The unknown parameters can then be learned with a gradient descent algorithm from the measurement data. We verify the effectiveness of our algorithm in a circuit QED system described by a Jaynes-Cumming model whose Hamiltonian identification has been rarely considered. We also show that our gradient algorithm can learn the spectrum of a non-Markovian environment based on an augmented system model.