# Combining the synergistic control capabilities of modelling and experiments: illustration of finding a minimum time quantum objective

## TL;DR

This paper demonstrates near time-optimal quantum state preparation using a combined approach of modeling and experimental optimization, achieving high fidelity in a practical NMR setup.

## Contribution

It introduces a synergistic method that integrates model-based numerical optimization with experimental learning to find minimal-time quantum controls.

## Key findings

- Achieved >99% fidelity in Bell state preparation
- Demonstrated the effectiveness of combined modeling and experimental control
- Potential for broad applications in quantum control optimization

## Abstract

A common way to manipulate a quantum system, for example spins or artificial atoms, is to use properly tailored control pulses. In order to accomplish quantum information tasks before coherence is lost, it is crucial to implement the control in the shortest possible time. Here we report the near time-optimal preparation of a Bell state with fidelity higher than $99\%$ in an NMR experiment, which is feasible by combining the synergistic capabilities of modelling and experiments operating in tandem. The pulses preparing the Bell state are found by experiments that are recursively assisted with a gradient-based optimization algorithm working with a model. Thus, we explore the interplay between model-based numerical optimal design and experimental-based learning control. Utilizing the balanced synergism between the dual approaches should have broad applications for accelerating the search for optimal quantum controls.