# Stochastic Estimation of Dynamical Variables

## TL;DR

The paper introduces STEADY, a robust stochastic estimation method for accurately determining the Hamiltonian of quantum systems, leveraging all measurement data and scalable to information-theoretic limits.

## Contribution

It presents a novel stochastic gradient descent-based estimator that efficiently and robustly estimates complete Hamiltonians of quantum systems, including non-unitary parameters.

## Key findings

- Performance scales at information-theoretic limits
- Robust to state preparation and measurement errors
- Applicable to piecewise-differentiable Hamiltonians

## Abstract

Estimating the parameters governing the dynamics of a system is a prerequisite for its optimal control. We present a simple but powerful method that we call STEADY, for STochastic Estimation algorithm for DYnamical variables, to estimate the Hamiltonian (or Lindbladian) governing a quantum system of a few qubits. STEADY makes efficient use of all measurements and its performance scales as the information-theoretic limits for such an estimator. Importantly, it is inherently robust to state preparation and measurement errors. It is not limited to evaluating only a fixed set of possible gates, rather it estimates the complete Hamiltonian of the system. The estimator is applicable to any Hamiltonian that can be written as a piecewise-differentiable function and it can easily include estimators for the non-unitary parameters as well. At the heart of our approach is a stochastic gradient descent over the difference between experimental measurement and model prediction.