Aitor Moreno Fdez. de Leceta

Alejandro Mata Ali, Aitor Moreno Fdez. de Leceta, Jorge López Rubio

We present a series of algorithms in tensor networks for anomaly detection in datasets, by using data compression in a Tensor Train representation. These algorithms consist of preserving the structure of normal data in compression and deleting the structure of anomalous data. The algorithms can be applied to any tensor network representation. We test the effectiveness of the methods with digits and Olivetti faces datasets and a cybersecurity dataset to determine cyber-attacks.

Alejandro Mata Ali, Iñigo Perez Delgado, Beatriz García Markaida et al.

This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while minimizing the total execution cost. With this method, an exact and explicit solution of the problem is provided. This algorithm constructs a tensor network representation of the tensor which provides the solution of the problem. This method is improved in order to reduce the computational complexity of the solution computation, using problem preprocessing, new techniques of condensation of logical constraints, optimization of the value determination technique with previously calculated results, reuse of intermediate computations, and iterative relations for constraints. Three algorithms for computation are presented: the main algorithm, the iterative algorithm which adds only the minimal amount of necessary constraints, and the genetic algorithm which combines the iterative algorithm with basic genetic algorithms. Finally, a simple version of both algorithms was implemented, and their performance was tested, all publicly available.

Alejandro Mata Ali, Iñigo Perez Delgado, Aitor Moreno Fdez. de Leceta

This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces constraints through explicit counting filters. This formalism also yields an explicit tensor-network marginal formula whose zero-temperature, exact-arithmetic limit identifies an optimal feasible tour through a sequential marginal rule. At finite $τ$ and finite precision, the implemented extraction is a heuristic whose behavior depends on numerical contrast, calibration, and near-degeneracies. We adapt the construction to several generalizations of the TSP and apply it to the Job Reassignment Problem, as a representative industrial integration. The experiments are deliberately small and illustrative; they contextualize the method against exact and heuristic references but do not establish general computational superiority over specialized classical solvers.

Alejandro Mata Ali, Iñigo Perez Delgado, Marina Ristol Roura et al.

We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and lineal entrywise norms, depending on the type of tensor network involved. The core of this method is the use of the norm of subnetworks of the tensor network in an iterative way, so that we normalize by the finite values of the norms that led to the divergence or zero norm. In addition, the method benefits from the reuse of intermediate calculations. We have also applied it to the Matrix Product State/Tensor Train (MPS/TT) and Matrix Product Operator/Tensor Train Matrix (MPO/TT-M) layers and have seen its scaling versus the number of nodes, bond dimension, and physical dimension. All code is publicly available.

Alejandro Mata Ali, Iñigo Perez Delgado, Aitor Moreno Fdez. de Leceta

In this paper we present a study of the applicability and feasibility of quantum-inspired algorithms and techniques in tensor networks for industrial environments and contexts, with a compilation of the available literature and an analysis of the use cases that may be affected by such methods. In addition, we explore the limitations of such techniques in order to determine their potential scalability.

Alejandro Mata Ali, Iñigo Perez Delgado, Aitor Moreno Fdez. de Leceta

In this paper we present a study of the applicability and feasibility of quantum-inspired algorithms and techniques in tensor networks for industrial environments and contexts, with a compilation of the available literature and an analysis of the use cases that may be affected by such methods. In addition, we explore the limitations of such techniques in order to determine their potential scalability.