Compensating for non-linear distortions in controlled quantum systems

TL;DR

This paper introduces a quadratic estimation method to accurately model and compensate for non-linear, frequency-dependent distortions in control signals for quantum systems, improving the fidelity of quantum operations.

Contribution

The paper presents a novel quadratic estimation technique for non-linear transfer functions in quantum control, enabling better compensation of distortions using spectral training data.

Findings

Successfully tested on a Rydberg atom system

Improved control fidelity in quantum experiments

Effective for non-linear transfer functions of arbitrary length

Abstract

Predictive design and optimization methods for controlled quantum systems depend on the accuracy of the system model. Any distortion of the input fields in an experimental platform alters the model accuracy and eventually disturbs the predicted dynamics. These distortions can be non-linear with a strong frequency dependence so that the field interacting with the microscopic quantum system has limited resemblance to the input signal. We present an effective method for estimating these distortions which is suitable for non-linear transfer functions of arbitrary lengths and magnitudes provided the available training data has enough spectral components. Using a quadratic estimation, we have successfully tested our approach for a numerical example of a single Rydberg atom system. The transfer function estimated from the presented method is incorporated into an open-loop control optimization algorithm allowing for high-fidelity operations in quantum experiments.