# Quantum Hamiltonian Identification with Classical Colored Measurement Noise

## TL;DR

This paper introduces a method for identifying quantum Hamiltonians in closed systems affected by classical colored measurement noise, using an augmented system model and eigenstate realization to accurately estimate unknown parameters.

## Contribution

It presents a novel Hamiltonian identification approach that accounts for classical colored measurement noise via an augmented system model and transfer-function techniques.

## Key findings

- Effective identification of quantum Hamiltonians with colored noise
- Verification on a two-qubit system demonstrates accuracy
- Method improves robustness against measurement disturbances

## Abstract

In this paper, we present a Hamiltonian identification method for a closed quantum system whose time trace observables are measured with colored measurement noise. The dynamics of the quantum system are described by a Liouville equation which can be converted to a coherence vector representation. Since the measurement process is disturbed by classical colored noise, we introduce an augmented system model to describe the total dynamics, where the classical colored noise is parameterized. Based on the augmented system model as well as the measurement data, we can find a realization of the quantum system with unknown parameters by employing an Eigenstate Realization Algorithm. The unknown parameters can be identified using a transfer-function-based technique. An example of a two-qubit system with colored measurement noise is demonstrated to verify the effectiveness of our method.