# Evolution-free Hamiltonian parameter estimation through Zeeman markers

## TL;DR

This paper introduces a method for estimating Hamiltonian parameters using only spectral shifts caused by local Zeeman fields, eliminating the need for time-dependent measurements and demonstrating broad applicability.

## Contribution

It presents a novel, evolution-free protocol for Hamiltonian estimation based solely on spectral shifts from Zeeman markers, applicable to various quantum systems.

## Key findings

- Protocol works with simple tight-binding models
- Demonstrates stability under Gaussian noise
- Applicable to diverse quantum systems

## Abstract

We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured, it fully suffices to observe spectral shifts induced by fields applied to local `markers'. We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations.