# Multi-objective Optimization in Quantum Parameter Estimation

## TL;DR

This paper explores multi-objective optimization strategies for quantum parameter estimation, balancing precision enhancement via control techniques with preservation of system fidelity in open quantum systems.

## Contribution

It introduces a multi-objective model that optimizes Fisher information and system state deformation, demonstrating the effectiveness of Hamiltonian control through simulations.

## Key findings

- Improved estimation precision with control methods.
- Trade-off between Fisher information and system fidelity.
- Feasibility of Hamiltonian control demonstrated.

## Abstract

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified {\epsilon}-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.