Iker Pastor-López

Matrix product operators (MPOs) are a standard representation for structured operators in tensor-network simulations and quantum computing applications. However, converting symbolic descriptions of Hamiltonians and cost functions into MPO representations often requires substantial manual implementation, making the process error-prone and difficult to reproduce. This paper presents autotn, an open-source Python software tool that converts symbolic operator rules into MPO representations. Users define local operators and interaction rules in a high-level format, and the software generates the corresponding MPO along with validation utilities. In doing so, the software follows an automata-inspired approach that identifies repeated patterns in the symbolic description of the operator and reuses them to build a compact tensor-network representation, avoiding the need to construct each tensor by hand. The current implementation of autotn supports both diagonal operators, commonly encountered in combinatorial optimization problems, and general local matrix operators used in quantum many-body physics. The software is demonstrated on Max-Cut cost operators, long-range XX+YY+Z spin Hamiltonians, and quantum clock models. By providing a reproducible workflow from symbolic model specification to validated MPO construction, autotn reduces the engineering effort required to develop, verify, and compare MPO constructions.

Matrix product operators (MPOs) are a standard representation for structured operators in tensor-network simulations and quantum computing applications. However, converting symbolic descriptions of Hamiltonians and cost functions into MPO representations often requires substantial manual implementation, making the process error-prone and difficult to reproduce. This paper presents autotn, an open-source Python software tool that converts symbolic operator rules into MPO representations. Users define local operators and interaction rules in a high-level format, and the software generates the corresponding MPO along with validation utilities. In doing so, the software follows an automata-inspired approach that identifies repeated patterns in the symbolic description of the operator and reuses them to build a compact tensor-network representation, avoiding the need to construct each tensor by hand. The current implementation of autotn supports both diagonal operators, commonly encountered in combinatorial optimization problems, and general local matrix operators used in quantum many-body physics. The software is demonstrated on Max-Cut cost operators, long-range XX+YY+Z spin Hamiltonians, and quantum clock models. By providing a reproducible workflow from symbolic model specification to validated MPO construction, autotn reduces the engineering effort required to develop, verify, and compare MPO constructions.

Accurately evaluating positivity in social media profiles has important implications for advertising, mental health monitoring, and responsible AI applications. However, the multimodal nature of Instagram, where images, captions, hashtags, and emojis co-occur, challenges conventional unimodal sentiment analysis tools. We present a multimodal system that integrates computer vision and natural language processing to assess Instagram profiles. The architecture comprises two blocks: (i) feature extraction via facial-emotion analysis, object detection, chromatic cues, and linguistic processing; and (ii) profile-level inference, which fuses aggregated features to produce an overall positivity score together with semantically meaningful profile tags. Experiments on public Instagram profiles (images, captions, and comments), including an expert-annotated subset of comments, compare unimodal baselines with transformer-based embeddings and OpenAI large language models. The multimodal pipeline improves over unimodal variants, and the OpenAI approach achieves higher concordance with expert judgements than RoBERTa/Bi-LSTM baselines. Beyond technical contributions, we discuss privacy, transparency, and misuse risks associated with affective computing on social media. The proposed framework contributes to the advancement of multimodal sentiment analysis in social media and highlights its applicability to areas such as marketing analytics, well-being monitoring, and ethically aligned AI systems.

Fractional-order systems capture complex dynamic behaviors more accurately than integer-order models, yet their real-time identification remains challenging, particularly in resource-constrained environments. This work proposes a hybrid framework that combines Particle Swarm Optimization (PSO) with various artificial intelligence (AI) techniques to estimate reduced-order models of fractional systems. First, PSO optimizes model parameters by minimizing the discrepancy between the high-order system response and the reduced model output. These optimized parameters then serve as training data for several AI-based algorithms—including neural networks, support vector regression (SVR), and extreme gradient boosting (XGBoost)—to evaluate their inference speed and accuracy. Experimental validation on a custom-built heating system demonstrates that both PSO and the AI techniques yield precise reduced-order models. While PSO achieves slightly lower error metrics, its iterative nature leads to higher and more variable computation times compared to the deterministic and rapid inference of AI approaches. These findings highlight a trade-off between estimation accuracy and computational efficiency, providing a robust solution for real-time fractional-order system identification on edge devices.

Combinatorial optimization is essential across numerous disciplines. Traditional metaheuristics excel at exploring complex solution spaces efficiently, yet they often struggle with scalability. Deep learning has become a viable alternative for quickly generating high-quality solutions, particularly when metaheuristics underperform. In recent years, quantum-inspired approaches such as tensor networks have shown promise in addressing these challenges. Despite these advancements, a thorough comparison of the different paradigms is missing. This study evaluates eight algorithms on Weighted Max-Cut graphs ranging from 10 to 250 nodes. Specifically, we compare a Genetic Algorithm representing metaheuristics, a Graph Neural Network for deep learning, and the Density Matrix Renormalization Group as a tensor network approach. Our analysis focuses on solution quality and computational efficiency (i.e., time and memory usage). Numerical results show that the Genetic Algorithm achieves near-optimal results for small graphs, although its computation time grows significantly with problem size. The Graph Neural Network offers a balanced solution for medium-sized instances with low memory demands and rapid inference, yet it exhibits more significant variability on larger graphs. Meanwhile, the Tensor Network approach consistently yields high approximation ratios and efficient execution on larger graphs, albeit with increased memory consumption.