Gorka Muñoz-Gil

Paulin de Schoulepnikoff, Hendrik Poulsen Nautrup, Hans J. Briegel et al.

Interpretable machine learning techniques are becoming essential tools for extracting physical insights from complex quantum data. We build on recent advances in variational autoencoders to demonstrate that such models can learn physically meaningful and interpretable representations from a broad class of unlabeled quantum datasets. From raw measurement data alone, the learned representation reveals rich information about the underlying structure of quantum phase spaces. We further augment the learning pipeline with symbolic methods, enabling the discovery of compact analytical descriptors that serve as order parameters for the distinct regimes emerging in the learned representations. We demonstrate the framework on experimental Rydberg-atom snapshots, classical shadows of the cluster Ising model, and hybrid discrete-continuous fermionic data, revealing previously unreported phenomena such as a corner-ordering pattern in the Rydberg arrays. These results establish a general framework for the automated and interpretable discovery of physical laws from diverse quantum datasets. All methods are available through qdisc, an open-source Python library designed to make these tools accessible to the broader community.

Florian Fürrutter, Gorka Muñoz-Gil, Hans J. Briegel

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.

Gabriel Fernández-Fernández, Carlo Manzo, Maciej Lewenstein et al.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $β$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

Gorka Muñoz-Gil, Andrea López-Incera, Lukas J. Fiderer et al.

The foraging behavior of animals is a paradigm of target search in nature. Understanding which foraging strategies are optimal and how animals learn them are central challenges in modeling animal foraging. While the question of optimality has wide-ranging implications across fields such as economy, physics, and ecology, the question of learnability is a topic of ongoing debate in evolutionary biology. Recognizing the interconnected nature of these challenges, this work addresses them simultaneously by exploring optimal foraging strategies through a reinforcement learning framework. To this end, we model foragers as learning agents. We first prove theoretically that maximizing rewards in our reinforcement learning model is equivalent to optimizing foraging efficiency. We then show with numerical experiments that, in the paradigmatic model of non-destructive search, our agents learn foraging strategies which outperform the efficiency of some of the best known strategies such as Lévy walks. These findings highlight the potential of reinforcement learning as a versatile framework not only for optimizing search strategies but also to model the learning process, thus shedding light on the role of learning in natural optimization processes.

Gorka Muñoz-Gil, Hendrik Poulsen Nautrup, Arunava Majumder et al.

Learning interpretable representations with variational autoencoders (VAEs) is a major goal of representation learning. The main challenge lies in obtaining disentangled representations, where each latent dimension corresponds to a distinct generative factor. This difficulty is fundamentally tied to the inability to perform nonlinear independent component analysis. Here, we introduce the framework of action-induced representations (AIRs) which models representations of physical systems given experiments (or actions) that can be performed on them. We show that, in this framework, we can provably disentangle degrees of freedom w.r.t. their action dependence. We further introduce a variational AIR architecture (VAIR) that can extract AIRs and therefore achieve provable disentanglement where standard VAEs fail. Beyond state representation, VAIR also captures the action dependence of the underlying generative factors, directly linking experiments to the degrees of freedom they influence.

Maud van Lier, Gorka Muñoz-Gil

The arrival of Large Language Models (LLMs) has stirred up philosophical debates about the possibility of realizing agency in an artificial manner. In this work we contribute to the debate by presenting a theoretical model that can be used as a threshold conception for artificial agents. The model defines agents as systems whose actions and goals are always influenced by a dynamic framework of factors that consists of the agent's accessible history, its adaptive repertoire and its external environment. This framework, in turn, is influenced by the actions that the agent takes and the goals that it forms. We show with the help of the model that state-of-the-art LLMs are not agents yet, but that there are elements to them that suggest a way forward. The paper argues that a combination of the agent architecture presented in Park et al. (2023) together with the use of modules like the Coscientist in Boiko et al. (2023) could potentially be a way to realize agency in an artificial manner. We end the paper by reflecting on the obstacles one might face in building such an artificial agent and by presenting possible directions for future research.

Przemysław R. Grzybowski, Antoni Jankiewicz, Eloy Piñol et al.

It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be numerically hard. Recently we proposed a regularisation of the connections of Boltzmann machines, in order to control the energy landscape of the model, paving a way for efficient sampling and training. Here we formally prove that such regularised Boltzmann machines preserve the ability to represent arbitrary distributions. This is in conjunction with controlling the number of energy local minima, thus enabling easy \emph{guided} sampling and training. Furthermore, we explicitly show that regularised Boltzmann machines can store exponentially many arbitrarily correlated visible patterns with perfect retrieval, and we connect them to the Dense Associative Memory networks.

Giovanni Acampora, Andris Ambainis, Natalia Ares et al.

This white paper discusses and explores the various points of intersection between quantum computing and artificial intelligence (AI). It describes how quantum computing could support the development of innovative AI solutions. It also examines use cases of classical AI that can empower research and development in quantum technologies, with a focus on quantum computing and quantum sensing. The purpose of this white paper is to provide a long-term research agenda aimed at addressing foundational questions about how AI and quantum computing interact and benefit one another. It concludes with a set of recommendations and challenges, including how to orchestrate the proposed theoretical work, align quantum AI developments with quantum hardware roadmaps, estimate both classical and quantum resources - especially with the goal of mitigating and optimizing energy consumption - advance this emerging hybrid software engineering discipline, and enhance European industrial competitiveness while considering societal implications.

Paulin de Schoulepnikoff, Gorka Muñoz-Gil, Hendrik Poulsen Nautrup et al.

Interpretable machine learning is rapidly becoming a crucial tool for scientific discovery. Among existing approaches, variational autoencoders (VAEs) have shown promise in extracting the hidden physical features of some input data, with no supervision nor prior knowledge of the system at study. Yet, the ability of VAEs to create meaningful, interpretable representations relies on their accurate approximation of the underlying probability distribution of their input. When dealing with quantum data, VAEs must hence account for its intrinsic randomness and complex correlations. While VAEs have been previously applied to quantum data, they have often neglected its probabilistic nature, hindering the extraction of meaningful physical descriptors. Here, we demonstrate that two key modifications enable VAEs to learn physically meaningful latent representations: a decoder capable of faithfully reproduce quantum states and a probabilistic loss tailored to this task. Using benchmark quantum spin models, we identify regimes where standard methods fail while the representations learned by our approach remain meaningful and interpretable. Applied to experimental data from Rydberg atom arrays, the model autonomously uncovers the phase structure without access to prior labels, Hamiltonian details, or knowledge of relevant order parameters, highlighting its potential as an unsupervised and interpretable tool for the study of quantum systems.

Gorka Muñoz-Gil, Hans J. Briegel, Michele Caraglio

Target search problems are central to a wide range of fields, from biological foraging to the optimization algorithms. Recently, the ability to reset the search has been shown to significantly improve the searcher's efficiency. However, the optimal resetting strategy depends on the specific properties of the search problem and can often be challenging to determine. In this work, we propose a reinforcement learning (RL)-based framework to train agents capable of optimizing their search efficiency in environments by learning how to reset. First, we validate the approach in a well-established benchmark: the Brownian search with resetting. There, RL agents consistently recover strategies closely resembling the sharp resetting distribution, known to be optimal in this scenario. We then extend the framework by allowing agents to control not only when to reset, but also their spatial dynamics through turning actions. In this more complex setting, the agents discover strategies that adapt both resetting and turning to the properties of the environment, outperforming the proposed benchmarks. These results demonstrate how reinforcement learning can serve both as an optimization tool and a mechanism for uncovering new, interpretable strategies in stochastic search processes with resetting.

Florian Fürrutter, Zohim Chandani, Ikko Hamamura et al.

Efficiently compiling quantum operations remains a major bottleneck in scaling quantum computing. Today's state-of-the-art methods achieve low compilation error by combining search algorithms with gradient-based parameter optimization, but they incur long runtimes and require multiple calls to quantum hardware or expensive classical simulations, making their scaling prohibitive. Recently, machine-learning models have emerged as an alternative, though they are currently restricted to discrete gate sets. Here, we introduce a multimodal denoising diffusion model that simultaneously generates a circuit's structure and its continuous parameters for compiling a target unitary. It leverages two independent diffusion processes, one for discrete gate selection and one for parameter prediction. We benchmark the model over different experiments, analyzing the method's accuracy across varying qubit counts, circuit depths, and proportions of parameterized gates. Finally, by exploiting its rapid circuit generation, we create large datasets of circuits for particular operations and use these to extract valuable heuristics that can help us discover new insights into quantum circuit synthesis.

Frederik Møller, Gabriel Fernández-Fernández, Thomas Schweigler et al.

Analog quantum simulators provide access to many-body dynamics beyond the reach of classical computation. However, extracting physical insights from experimental data is often hindered by measurement noise, limited observables, and incomplete knowledge of the underlying microscopic model. Here, we develop a machine learning approach based on a variational autoencoder (VAE) to analyze interference measurements of tunnel-coupled one-dimensional Bose gases, which realize the sine-Gordon quantum field theory. Trained in an unsupervised manner, the VAE learns a minimal latent representation that strongly correlates with the equilibrium control parameter of the system. Applied to non-equilibrium protocols, the latent space uncovers signatures of frozen-in solitons following rapid cooling, and reveals anomalous post-quench dynamics not captured by conventional correlation-based methods. These results demonstrate that generative models can extract physically interpretable variables directly from noisy and sparse experimental data, providing complementary probes of equilibrium and non-equilibrium physics in quantum simulators. More broadly, our work highlights how machine learning can supplement established field-theoretical techniques, paving the way for scalable, data-driven discovery in quantum many-body systems.

Gorka Muñoz-Gil, Guillem Guigó i Corominas, Maciej Lewenstein

The characterization of diffusion processes is a keystone in our understanding of a variety of physical phenomena. Many of these deviate from Brownian motion, giving rise to anomalous diffusion. Various theoretical models exists nowadays to describe such processes, but their application to experimental setups is often challenging, due to the stochastic nature of the phenomena and the difficulty to harness reliable data. The latter often consists on short and noisy trajectories, which are hard to characterize with usual statistical approaches. In recent years, we have witnessed an impressive effort to bridge theory and experiments by means of supervised machine learning techniques, with astonishing results. In this work, we explore the use of unsupervised methods in anomalous diffusion data. We show that the main diffusion characteristics can be learnt without the need of any labelling of the data. We use such method to discriminate between anomalous diffusion models and extract their physical parameters. Moreover, we explore the feasibility of finding novel types of diffusion, in this case represented by compositions of existing diffusion models. At last, we showcase the use of the method in experimental data and demonstrate its advantages for cases where supervised learning is not applicable.

Alejandro Pozas-Kerstjens, Gorka Muñoz-Gil, Eloy Piñol et al.

We introduce a new family of energy-based probabilistic graphical models for efficient unsupervised learning. Its definition is motivated by the control of the spin-glass properties of the Ising model described by the weights of Boltzmann machines. We use it to learn the Bars and Stripes dataset of various sizes and the MNIST dataset, and show how they quickly achieve the performance offered by standard methods for unsupervised learning. Our results indicate that the standard initialization of Boltzmann machines with random weights equivalent to spin-glass models is an unnecessary bottleneck in the process of training. Furthermore, this new family allows for very easy access to low-energy configurations, which points to new, efficient training algorithms. The simplest variant of such algorithms approximates the negative phase of the log-likelihood gradient with no Markov chain Monte Carlo sampling costs at all, and with an accuracy sufficient to achieve good learning and generalization.

Gorka Muñoz-Gil, Miguel Angel Garcia-March, Carlo Manzo et al.

In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion, and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate even very short trajectories to the underlying diffusion mechanism with a high accuracy. In addition, the method is able to classify the motion according to normal or anomalous diffusion, and determine its anomalous exponent with a small error. The method provides highly accurate outputs even when working with very short trajectories and in the presence of experimental noise. We further demonstrate the application of transfer learning to experimental and simulated data not included in the training/testing dataset. This allows for a full, high-accuracy characterization of experimental trajectories without the need of any prior information.