Abstract Machine learning (ML) techniques applied to quantum many-body physics have emerged as a new research field. While the numerical power of this approach is undeniable, the most expressive ML algorithms, such as neural networks, are black boxes: The user does neither know the logic behind the model predictions nor the uncertainty of the model predictions. In this work, we present a toolbox for interpretability and reliability, agnostic of the model architecture. In particular, it provides a notion of the influence of the input data on the prediction at a given test point, an estimation of the uncertainty of the model predictions, and an extrapolation score for the model predictions. Such a toolbox only requires a single computation of the Hessian of the training loss function. Our work opens the road to the systematic use of interpretability and reliability methods in ML applied to physics and, more generally, science.
Abstract Machine learning (ML) techniques applied to quantum many-body physics have emerged as a new research field. While the numerical power of this approach is undeniable, the most expressive ML algorithms, such as neural networks, are black boxes: The user does neither know the logic behind the model predictions nor the uncertainty of the model predictions. In this work, we present a toolbox for interpretability and reliability, agnostic of the model architecture. In particular, it provides a notion of the influence of the input data on the prediction at a given test point, an estimation of the uncertainty of the model predictions, and an extrapolation score for the model predictions. Such a toolbox only requires a single computation of the Hessian of the training loss function. Our work opens the road to the systematic use of interpretability and reliability methods in ML applied to physics and, more generally, science.
The “black-box” nature of deep learning models fundamentally limits their reliability in critical applications. Tensor networks (TNs), drawing on their interpretable, quantum-probabilistic foundations, offer a promising pathway toward more transparent machine learning (ML). However, a systematic understanding of their capabilities and limitations remains an open challenge. Here, we establish a fundamental connection between a core property of quantum systems, namely, the catastrophe of orthogonality (COO), and the representational power and generalization performance of quantum-probabilistic TN models. Taking the Fashion Modified National Institute of Standards and Technology dataset, we propose 2 multiqubit data encoding schemes and demonstrate that key hyperparameters, such as the number of qubits, feature count, and mapping angle, modulate the onset of COO. This control mechanism directly dictates the model’s capacity, revealing that over-fitting can be interpreted as a specific regime of the quantum state space. Our work provides a theoretical lens, grounded in quantum many-body physics, for interpreting ML models. It positions TNs not merely as efficient computational tools but as a foundational framework for building inherently interpretable and reliable ML models.
Abstract The interplay between machine learning and quantum computing can lead to unprecedented prospects for both fundamental research and real-world applications. In this new field of quantum machine learning, quantum classifiers, i.e., quantum algorithms for solving classification problems, have attracted the most attention. However, despite the promising performance of these new models for classification tasks, they are complex black-box models. Therefore, like or even more so than classical machine learning models, their use in critical contexts such as medical diagnosis could be hampered without the support of explanations. This paper addresses this challenge by investigating the use of Local Interpretable Model-agnostic Explanations (LIME) for quantum classifiers, with a specific focus on the stability of the explanations. Stability is a key property for ensuring that explanations are consistent and trustworthy, especially when decisions impact sensitive domains. The paper conducts a systematic stability study of LIME in the quantum setting, validating whether a classical explainable AI technique can be meaningfully applied to quantum models. As shown in experiments involving different datasets belonging to critical applications, LIME provides explanations for quantum support vector machines and quantum neural networks that are not only interpretable but also stable. By highlighting the stability of explanations, these findings demonstrate the suitability of LIME as an explainability tool for quantum classifiers.
Abstract Despite the complexity of quantum systems in the real world, models with just a few effective many-body states often suffice to describe their quantum dynamics, provided decoherence is accounted for. We show that a machine learning algorithm is able to construct such models, given a straightforward set of quantum dynamics measurements. The effective Hilbert space can be a black box, with variations of the coupling to just one accessible output state being sufficient to generate the required training data. We demonstrate through simulations of a Markovian open quantum system that a neural network can automatically detect the number N of effective states and the most relevant Hamiltonian terms and state-dephasing processes and rates. For systems with N ⩽ 5 we find typical mean relative errors of predictions in the 10 % range. With more advanced networks and larger training sets, it is conceivable that a future single software can provide the automated first stop solution to model building for an unknown device or system, complementing and validating the conventional approach based on physical insight into the system.
Recently there is an increasing interest in applying machine learning algorithm to physics problems. These applications provide new platforms to challenge the critical issue of how to uncover the black box of machine learning because there always exists well-defined rules under physics problems. The success of such efforts can offer great promise of discovering new physics from experimental data by artificial intelligence. As a benchmark and a proof-of-principle study that this approach is indeed possible, in this work we design an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schr\odinger equation from simulated experimental data of the potential-to-density mappings of a quantum particle. This introspective learning architecture contains a translator and a knowledge distiller. The translator employs a recurrent neural network to learn the potential to density mapping, and the knowledge distiller applies the auto-encoder to extract the essential information and its update law from the hidden layer of the translator, which turns out to be the quantum wave function and the Schr\odinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.
In this digital age, machine learning (a prominent element within the context of artificial intelligence) has become an integral part of modern life, influencing various aspects of our daily activities.The predictive power of these tools is increasing with the advancements in algorithms, increased computational power, and the availability of large data sets: one basic example of this is language-based models, which have revolutionized our capabilities of transferring and processing information.Data is the foundational element of machine learning, and the quality and relevance of the data sets have a profound impact on the performance and accuracy of machine learning models.Thus "data is the new gold", captures the immense value that data holds in our modern world.With the exponential growth in data, the increasing demand for better machine-learning tools comes as a natural consequence.The field of physics is no exception to this, especially with the rise of big simulations and experiments generating huge amounts of data.Experiments at particle accelerators like the Large Hadron Collider(LHC) and Fermi lab, gravitational waves detector by LIGO and Virgo, climate models and weather simulations, Sloan Digital Sky Survey (SDSS), Cosmic Microwave Background(CMB) radiation providing insights into the early universe; all these studies generate massive data sets.In this context, developing more powerful, accurate, and specialized tools, is essential to meet the evolving needs in physics as well.In this thesis, we aim to study different types of ML tools to characterize the many-body problem in the context of classical and quantum statistical mechanics, with a focus on unbiased and interpretable methods.We use techniques coming from so-called non-parametric learning (NPL), where the analysis is done without specifying a fixed set of parameters in an assumption-free vi manner.NPL is a subset of the broad unsupervised learning category; the algorithm learns from the intrinsic structure of the data set.NPL is particularly valuable in scenarios where data assumptions are uncertain, data distributions are non-standard, or when dealing with complex data sets where relationships are difficult to predict beforehand.This works in our favor as the relation between data sets coming from many-body physics system and their effect on data structures when physical parameters change is not well understood -the simple reason being that the typical physicists mindset is very much focused on performing huge dimensional reduction from microscopic physical information (a canonical example of this being mean field theories, where the behavior of a large number of degrees of freedom is replaced by a single one).The thesis is organized as follows.In Chapter 1, we discuss the theoretical framework behind the NPL methods used.We present basic ideas in our methodologies, which encompass the overarching principles guiding our approach.These include the linkage between statistical physics and data analysis, particularly in relation to intrinsic dimension (Id) and its significance in understanding critical characteristics.Additionally, we delve into the application of Principal Component Analysis (PCA) and introduce the notion of PCA entropy -a witness of information spreading under linear transformation, whose relevance to physical phenomena we start investigating here.In Chapter 2, we describe the data sets we work with; statistical mechanics inspired data sets, such as those generated via sampling classical Ising models through advanced Monte Carlo algorithms, and experimental data of a spinor Bose-Einstein condensate.The following chapters present the applications I worked on.In Chapter 3, we present and thoroughly assess a framework for understanding critical behavior in classical partition functions by employing NPL techniques on data sets containing thermal configurations; provide a robust analysis of phase transitions using different NPL methods.In Chapter 4, we present a theoretical framework for information extraction in synthetic quantum matter for the case of a quantum quench in a spinor Bose-Einstein vii condensate experiment.In Chapter 5, we demonstrate how the field of network science can significantly improve and elevate our assumption-free characterization of various phases of matter.We present compelling evidence that network science offers a transparent and effective set of methods for investigating the properties of distinct phases and phase transitions, enabling us to identify critical points.
Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages quantum mechanical principles to accelerate machine learning tasks.Despite its potential, most QML models remain opaque "black boxes," hindering their deployment in high-stakes or regulated domains where trust and accountability are essential.This work introduces two novel interpretability methods tailored for QML: Quantum Shapley Values (QSV) and Quantum Local Interpretable Model-Agnostic Explanations (Q-LIME).QSV adapts cooperative game theory to quantify the contribution of individual qubits, observables, or circuit parameters, while Q-LIME generates perturbed quantum states and trains surrogate classical models to approximate local decision boundaries.Through experiments on variational quantum classifiers and hybrid quantum-classical neural networks, we demonstrate that QSV provides rigorous attribution but suffers from scalability constraints, whereas Q-LIME yields efficient, approximate explanations suitable for near-term devices.By transforming quantum models from opaque "black boxes" into interpretable "glass boxes," this research lays the foundation for trustworthy, transparent, and human centred quantum AI.