This paper presents a strategy for efficient quantum circuit design for density estimation. The strategy is based on a quantum-inspired algorithm for density estimation and a circuit optimisation routine based on memetic algorithms. The model maps a training dataset to a quantum state represented by a density matrix through a quantum feature map. This training state encodes the probability distribution of the dataset in a quantum state, such that the density of a new sample can be estimated by projecting its corresponding quantum state onto the training state. We propose the application of a memetic algorithm to find the architecture and parameters of a variational quantum circuit that implements the quantum feature map, along with a variational learning strategy to prepare the training state. Demonstrations of the proposed strategy show an accurate approximation of the Gaussian kernel density estimation method through shallow quantum circuits illustrating the feasibility of the algorithm for near-term quantum hardware.

Reading comprehension continues to be a crucial research focus in the NLP community. Recent advances in Machine Reading Comprehension (MRC) have mostly centered on literal comprehension, referring to the surface-level understanding of content. In this work, we focus on the next level - interpretive comprehension, with a particular emphasis on inferring the themes of a narrative text. We introduce the first dataset specifically designed for interpretive comprehension of educational narratives, providing corresponding well-edited theme texts. The dataset spans a variety of genres and cultural origins and includes human-annotated theme keywords with varying levels of granularity. We further formulate NLP tasks under different abstractions of interpretive comprehension toward the main idea of a story. After conducting extensive experiments with state-of-the-art methods, we found the task to be both challenging and significant for NLP research.

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables. In quantum mechanics, a density matrix is the most general way to describe the state of a quantum system. This work extends the concept of density matrices by allowing them to be defined in a reproducing kernel Hilbert space. This abstraction allows the construction of differentiable models for density estimation, inference, and sampling, and enables their integration into end-to-end deep neural models. In doing so, we provide a versatile representation of marginal and joint probability distributions that allows us to develop a differentiable, compositional, and reversible inference procedure that covers a wide range of machine learning tasks, including density estimation, discriminative learning, and generative modeling. The broad applicability of the framework is illustrated by two examples: an image classification model that can be naturally transformed into a conditional generative model, and a model for learning with label proportions that demonstrates the framework's ability to deal with uncertainty in the training samples.

A central problem of quantum physics, be it fundamental quantum physics or applications for quantum technology, is the ground state problem. It can be defined as finding a state vector |Ψ that minimises the expected value of the Hamiltonian Ĥ that represents the energetic interactions between the different parts that make up a quantum physical system. It is well-known that the difficulty of solving the ground state problem for a physical system arises from the exponential growth of the Hilbert space with respect to the number of the system components and their dimension. Therefore, techniques such as exact diagonalisation of Ĥ quickly render insufficient to find the ground state, and other approximate methods have to be used. Interestingly, other central problems of quantum physics such as finding the evolution of a quantum system can be cast into the ground state problem, as demonstrated by the Feynman-Kitaev formalism [24]. An immediate implication of using this formalism is that the computational tools historically developed for solving the ground state problem can be used to find the dynamics of a physical system. Broadly speaking, the Feynman-Kitaev formalism appends a clock as an auxilliary subsystem of the main physical system, i.e. the Hilbert space H of the whole system is H = P C, where P is the Hilbert space of the main physical system and C is the Hilbert space of the clock.

Machine Learning (ML) is being used in multiple disciplines due to its powerful capability to infer relationships within data. In particular, Software Engineering (SE) is one of those disciplines in which ML has been used for multiple tasks, like software categorization, bugs prediction, and testing. In addition to the multiple ML applications, some studies have been conducted to detect and understand possible pitfalls and issues when using ML. However, to the best of our knowledge, only a few studies have focused on presenting ML best practices or guidelines for the application of ML in different domains. In addition, the practices and literature presented in previous literature (i) are domain-specific (e.g., concrete practices in biomechanics), (ii) describe few practices, or (iii) the practices lack rigorous validation and are presented in gray literature. In this paper, we present a study listing 127 ML best practices systematically mining 242 posts of 14 different Stack Exchange (STE) websites and validated by four independent ML experts. The list of practices is presented in a set of categories related to different stages of the implementation process of an ML-enabled system; for each practice, we include explanations and examples. In all the practices, the provided examples focus on SE tasks. We expect this list of practices could help practitioners to understand better the practices and use ML in a more informed way, in particular newcomers to this new area that sits at the intersection of software engineering and machine learning.

This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deep-learning models. The method combines an autoencoder, for learning a low-dimensional representation of the data, with a density-estimation model based on random Fourier features and density matrices in an end-to-end architecture that can be trained using gradient-based optimization techniques. The method predicts a degree of normality for new samples based on the estimated density. A systematic experimental evaluation was performed on different benchmark datasets. The experimental results show that the method performs on par with or outperforms other state-of-the-art methods.

Quantum computing has gained a lot of attention in recent years due to its potential to solve complex problems which would take exponential time in classical computers. Most of the research efforts have been focused on constructing quantum computers based on qubits [1]. However, there has been a growing interest in building quantum computers based on qudits, i.e. machines that simulate and operate d-dimensional quantum states, with d > 2. Various physical implementations of high-dimensional quantum states have been proposed, such as photonic states integrated in chips [2, 3], photonic modes encoded in the orbital angular momentum (OAM) [4], ion traps [5], ququarts implemented on a quadrupolar nuclear magnetic resonance (NMR) [6], and molecular quantum magnets [7]. Two of the main advantages of highdimensional quantum computers compared to their qubit-based counterparts are their larger information storage [8], and their higher resilience to noise [9]. One closely related field of quantum computing is quantum machine learning (QML). This field aims to develop novel quantum-inspired machine learning (ML) methods that may run on classical or quantum computers and to implement the existing ML algorithms on quantum computers. For instance, some classical machine learning algorithms like support vector machines and restricted Boltzmann machines can be implemented on qubit-based quantum computers [10, 11], and many of the ML methods have been reformulated in the language of quantum physics like quantum decision trees [12], quantum neural networks [13, 14], and quantum generative adversarial networks [15]. In contrast with QML methods built on qubits, less research has been done on QML based on qudits, i.e. algorithms that run in high-dimensional quantum computers. Some of these methods include protocols with qudits for reinforcement learning [16], and for training quantum neural networks [17, 18, 19].

This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the relationship between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the output. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings.

In this paper, we introduce the Dissimilarity Mixture Autoencoder (DMAE), a novel neural network model that uses a dissimilarity function to generalize a family of density estimation and clustering methods. It is formulated in such a way that it internally estimates the parameters of a probability distribution through gradient-based optimization. Also, the proposed model can leverage from deep representation learning due to its straightforward incorporation into deep learning architectures, because, it consists of an encoder-decoder network that computes a probabilistic representation. Experimental evaluation was performed on image and text clustering benchmark datasets showing that the method is competitive in terms of unsupervised classification accuracy and normalized mutual information. The source code to replicate the experiments is publicly available at https://github.com/larajuse/DMAE

The main goal of this paper is to explore latent topic analysis (LTA), in the context of quantum information retrieval. LTA is a valuable technique for document analysis and representation, which has been extensively used in information retrieval and machine learning. Different LTA techniques have been proposed, some based on geometrical modeling (such as latent semantic analysis, LSA) and others based on a strong statistical foundation. However, these two different approaches are not usually mixed. Quantum information retrieval has the remarkable virtue of combining both geometry and probability in a common principled framework. We built on this quantum framework to propose a new LTA method, which has a clear geometrical motivation but also supports a well-founded probabilistic interpretation. An initial exploratory experimentation was performed on three standard data sets. The results show that the proposed method outperforms LSA on two of the three datasets. These results suggests that the quantum-motivated representation is an alternative for geometrical latent topic modeling worthy of further exploration.