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, 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, 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.
Eneko Osaba, Esther Villar-Rodriguez, Izaskun Oregi et al.
Quantum Computing is an emerging paradigm which is gathering a lot of popularity in the current scientific and technological community. Widely conceived as the next frontier of computation, Quantum Computing is still at the dawn of its development. Thus, current solving systems suffer from significant limitations in terms of performance and capabilities. Some interesting approaches have been devised by researchers and practitioners in order to overcome these barriers, being quantum-classical hybrid algorithms one of the most often used solving schemes. The main goal of this paper is to extend the results and findings of the recently proposed hybrid Quantum Computing - Tabu Search Algorithm for partitioning problems. To do that, we focus our research on the adaptation of this method to the Asymmetric Traveling Salesman Problem. In overall, we have employed six well-known instances belonging to TSPLIB to assess the performance of Quantum Computing - Tabu Search Algorithm in comparison to QBSolv, a state-of-the-art decomposing solver. Furthermore, as an additional contribution, this work also supposes the first solving of the Asymmetric Traveling Salesman Problem using a Quantum Computing based method. Aiming to boost whole community's research in QC, we have released the project's repository as open source code for further application and improvements.
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.
Eneko Osaba, Esther Villar-Rodriguez, Izaskun Oregi et al.
Quantum Computing is considered as the next frontier in computing, and it is attracting a lot of attention from the current scientific community. This kind of computation provides to researchers with a revolutionary paradigm for addressing complex optimization problems, offering a significant speed advantage and an efficient search ability. Anyway, Quantum Computing is still in an incipient stage of development. For this reason, present architectures show certain limitations, which have motivated the carrying out of this paper. In this paper, we introduce a novel solving scheme coined as hybrid Quantum Computing - Tabu Search Algorithm. Main pillars of operation of the proposed method are a greater control over the access to quantum resources, and a considerable reduction of non-profitable accesses. To assess the quality of our method, we have used 7 different Traveling Salesman Problem instances as benchmarking set. The obtained outcomes support the preliminary conclusion that our algorithm is an approach which offers promising results for solving partitioning problems while it drastically reduces the access to quantum computing resources. We also contribute to the field of Transfer Optimization by developing an evolutionary multiform multitasking algorithm as initialization method.