Roy T. Forestano

Standard Bayesian retrievals for exoplanet atmospheric parameters from transmission spectroscopy, while well understood and widely used, are generally computationally expensive. In the era of the JWST and other upcoming observatories, machine learning approaches have emerged as viable alternatives that are both efficient and robust. In this paper we present a systematic study of several existing machine learning regression techniques and compare their performance for retrieving exoplanet atmospheric parameters from transmission spectra. We benchmark the performance of the different algorithms on the accuracy, precision, and speed. The regression methods tested here include partial least squares (PLS), support vector machines (SVM), k nearest neighbors (KNN), decision trees (DT), random forests (RF), voting (VOTE), stacking (STACK), and extreme gradient boosting (XGB). We also investigate the impact of different preprocessing methods of the training data on the model performance. We quantify the model uncertainties across the entire dynamical range of planetary parameters. The best performing combination of ML model and preprocessing scheme is validated on a the case study of JWST observation of WASP-39b.

Recursive Cartan decompositions (CDs) provide a way to exactly factorize quantum circuits into smaller components, making them a central tool for unitary synthesis. Here we present a detailed overview of recursive CDs, elucidating their mathematical structure, demonstrating their algorithmic utility, and implementing them numerically at large scales. We adapt, extend, and unify existing mathematical frameworks for recursive CDs, allowing us to gain new insights and streamline the construction of new circuit decompositions. Based on this, we show that several leading synthesis techniques from the literature-the Quantum Shannon, Block-ZXZ, and Khaneja-Glaser decompositions-implement the same recursive CD. We also present new recursive CDs based on the orthogonal and symplectic groups, and derive parameter-optimal decompositions. Furthermore, we aggregate numerical tools for CDs from the literature, put them into a common context, and complete them to allow for numerical implementations of all possible classical CDs in canonical form. As an application, we efficiently compile fast-forwardable Hamiltonian time evolution to fixed-depth circuits, compiling the transverse-field XY model on $10^3 qubits into 2 \times 10^6$ gates in 22 seconds on a laptop.

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, greatly motivate the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, one can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we perform a fair and comprehensive comparison between classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their AUC scores, the quantum networks were shown to outperform the classical networks. However, seeing the computational advantage of the quantum networks in practice may have to wait for the further development of quantum technology and its associated APIs.

A fundamental task in data science is the discovery, description, and identification of any symmetries present in the data. We developed a deep learning methodology for the simultaneous discovery of multiple non-trivial continuous symmetries across an entire labeled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function, ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to invariant transformations with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset, where the oracle is provided by the 10-dimensional vector of logits of a trained classifier. We find classes of symmetries that transform each image from the dataset into new synthetic images while conserving the values of the logits. We illustrate these transformations as lines of equal probability (“flows”) in the reduced latent space. These results show that symmetries in the data can be successfully searched for and identified as interpretable non-trivial transformations in the equivalent latent space.

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO(2), SO(3), and SO(4), and of the Lorentz group . Other examples include squeeze mapping, piecewise discontinuous labels, and SO(10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.