Carlos Cano

Ernesto Acosta, Guillermo Botella, Carlos Cano

Quantum annealers provide an effective framework for solving large-scale combinatorial optimization problems. This work presents a novel methodology for training Variational Quantum Algorithms (VQAs) by reformulating the parameter optimization task as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Unlike traditional gradient-based methods, our approach directly leverages the Hamiltonian of the chosen VQA ansatz and employs an adaptive, metaheuristic optimization scheme. This optimization strategy provides a rich set of configurable parameters which enables the adaptation to specific problem characteristics and available computational resources. The proposed framework is generalizable to arbitrary Hamiltonians and integrates a recursive refinement strategy to progressively approximate high-quality solutions. Experimental evaluations demonstrate the feasibility of the method and its ability to significantly reduce computational overhead compared to classical and evolutionary optimizers, while achieving comparable or superior solution quality. These findings suggest that quantum annealers can serve as a scalable alternative to classical optimizers for VQA training, particularly in scenarios affected by barren plateaus and noisy gradient estimates, and open new possibilities for hybrid quantum gate - quantum annealing - classical optimization models in near-term quantum computing.

Ana Martínez-Sabiote, Michalis Skotiniotis, Jara J. Bermejo-Vega et al.

This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus in bipartite systems of dimensions 3x3, 4x4, and 5x5, where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels we develop a classification scheme that distinguishes between separable states, PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching 80%, 90%, and nearly 100% for 3x3, 4x4, and 5x5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results establish machine learning as a powerful complement to traditional entanglement detection methods, particularly for higher-dimensional systems where conventional approaches become inadequate. The findings highlight key directions for future research, including hybrid quantum-classical implementations and improved data generation protocols to overcome current limitations.

Luca Cappelletti, Tommaso Fontana, Elena Casiraghi et al.

Graph Representation Learning (GRL) methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are beyond the capabilities of current methods and software implementations. We present GRAPE, a software resource for graph processing and embedding that can scale with big graphs by using specialized and smart data structures, algorithms, and a fast parallel implementation of random walk-based methods. Compared with state-of-the-art software resources, GRAPE shows an improvement of orders of magnitude in empirical space and time complexity, as well as a competitive edge and node label prediction performance. GRAPE comprises about 1.7 million well-documented lines of Python and Rust code and provides 69 node embedding methods, 25 inference models, a collection of efficient graph processing utilities and over 80,000 graphs from the literature and other sources. Standardized interfaces allow seamless integration of third-party libraries, while ready-to-use and modular pipelines permit an easy-to-use evaluation of GRL methods, therefore also positioning GRAPE as a software resource to perform a fair comparison between methods and libraries for graph processing and embedding.

Mauricio Soto-Gomez, Peter Robinson, Carlos Cano et al.

Many real-world problems are naturally modeled as heterogeneous graphs, where nodes and edges represent multiple types of entities and relations. Existing learning models for heterogeneous graph representation usually depend on the computation of specific and user-defined heterogeneous paths, or in the application of large and often not scalable deep neural network architectures. We propose Het-node2vec, an extension of the node2vec algorithm, designed for embedding heterogeneous graphs. Het-node2vec addresses the challenge of capturing the topological and structural characteristics of graphs and the semantic information underlying the different types of nodes and edges of heterogeneous graphs, by introducing a simple stochastic node and edge type switching strategy in second order random walk processes. The proposed approach also introduces an ''attention mechanism'' to focus the random walks on specific node and edge types, thus allowing more accurate embeddings and more focused predictions on specific node and edge types of interest. Empirical results on benchmark datasets show that Hetnode2vec achieves comparable or superior performance with respect to state-of-the-art methods for heterogeneous graphs in node label and edge prediction tasks.