# Designing quantum experiments with a genetic algorithm

## TL;DR

This paper presents a genetic algorithm for designing quantum optics experiments to create states with enhanced quantum Fisher information, demonstrating significant improvements over classical and Gaussian states, even under realistic noise conditions.

## Contribution

The paper introduces a flexible genetic algorithm for designing quantum experiments, capable of engineering non-Gaussian states with high quantum Fisher information for quantum metrology.

## Key findings

- Achieved up to 100-fold improvement over classical states.
- Engineered Schrödinger-cat-like states with around 80 photons.
- Found robust quantum states that outperform Gaussian states under noise.

## Abstract

We introduce a genetic algorithm that designs quantum optics experiments for engineering quantum states with specific properties. Our algorithm is powerful and flexible, and can easily be modified to find methods of engineering states for a range of applications. Here we focus on quantum metrology. First, we consider the noise-free case, and use the algorithm to find quantum states with a large quantum Fisher information (QFI). We find methods, which only involve experimental elements that are available with current or near-future technology, for engineering quantum states with up to a 100-fold improvement over the best classical state, and a 20-fold improvement over the optimal Gaussian state. Such states are a superposition of the vacuum with a large number of photons (around $80$), and can hence be seen as Schr\"odinger-cat-like states. We then apply the two most dominant noise sources in our setting -- photon loss and imperfect heralding -- and use the algorithm to find quantum states that still improve over the optimal Gaussian state with realistic levels of noise. This will open up experimental and technological work in using exotic non-Gaussian states for quantum-enhanced phase measurements. Finally, we use the Bayesian mean square error to look beyond the regime of validity of the QFI, finding quantum states with precision enhancements over the alternatives even when the experiment operates in the regime of limited data.