arXiv subjects

Alejandro Mata Ali

Publications and source records attributed to Alejandro Mata Ali.

At least 19 recordsLinked to original sources

arXiv2026

Visual-to-Code Authoring, Tensor-Network Debugging, and Quantum-Circuit Inspection Tools in Python

Tensor networks and quantum circuits are structural objects whose meaning depends on connectivity, indices, contraction order, gate placement, measurements, and related design choices. They are often easier to reason about visually than as code, yet in Python they are frequently constructed, transformed, and checked through backend-specific objects or compact symbolic expressions. This can make structural mistakes hard to notice during development, debugging, and communication. This paper presents three complementary packages: Tensor-Network-Visualization for visual debugging and structural inspection of supported tensor-network and traced einsum workflows; Tensor-Network-Editor for visual-to-code authoring, backend code generation, JSON preservation, export, and design-level analysis; and Quantum Circuit Drawer for clear circuit rendering, inspection, and complementary comparison of circuits or documented result distributions. The packages form a visual authoring and inspection layer around existing tensor-network libraries, array-based scientific Python workflows, and quantum SDKs. They are not simulators: they do not implement new contraction algorithms, execute quantum circuits, or guarantee full semantic equivalence across arbitrary backends. Their contribution is to make structural artifacts visible, editable, inspectable, comparable, exportable, and reproducible within those ecosystems.

quant-ph↗

arXiv2026

Quantum-inspired Tensor Network for QUBO, QUDO and Tensor QUDO Problems with k-neighbors

This work presents a novel tensor network algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, Quadratic Unconstrained Discrete Optimization (QUDO) problems, and Tensor Quadratic Unconstrained Discrete Optimization (T-QUDO) problems. The proposed algorithm is based on the MeLoCoToN methodology, which solves combinatorial optimization problems by employing superposition, imaginary time evolution, and projective measurements. Additionally, two different approaches are presented to solve QUBO and QUDO problems with k-neighbors interactions in a lineal chain, one based on 4-order tensor contraction and the other based on matrix-vector multiplication, including sparse computation and a new technique called "Waterfall". Furthermore, the performance of both implementations is compared with a quadratic optimization solver to demonstrate the performance of the method, showing advantages in several problem instances.

cs.DS↗

arXiv2025

Optimization of the quantization of dense neural networks from an exact QUBO formulation

This work introduces a post-training quantization (PTQ) method for dense neural networks via a novel ADAROUND-based QUBO formulation. Using the Frobenius distance between the theoretical output and the dequantized output (before the activation function) as the objective, an explicit QUBO whose binary variables represent the rounding choice for each weight and bias is obtained. Additionally, by exploiting the structure of the coefficient QUBO matrix, the global problem can be exactly decomposed into $n$ independent subproblems of size $f+1$, which can be efficiently solved using some heuristics such as simulated annealing. The approach is evaluated on MNIST, Fashion-MNIST, EMNIST, and CIFAR-10 across integer precisions from int8 to int1 and compared with a round-to-nearest traditional quantization methodology.

cs.LG↗

arXiv2025

Prime Factorization Equation from a Tensor Network Perspective

This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which addresses combinatorial optimization problems through classical tensor networks. The presented tensor network tensorizes a binary multiplication circuit and projects its output onto the target integer to be factorized. Additionally, in order to make the algorithm more efficient, the number and dimension of the tensors and their contraction scheme are optimized, including a reduced auxiliary register that still preserves at least one valid factorization orientation. Finally, a series of tests on the algorithm are conducted, contracting the tensor network both exactly and approximately using tensor train compression, and evaluating its performance.

math.OC↗

arXiv2025

Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective

In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal solution of the problems. As in other tensor network algorithms for combinatorial optimization problems, the method is based on imaginary time evolution and the implementation of restrictions in the tensor network. In addition, we introduce the use of symmetries and the reutilization of intermediate calculations, reducing the computational complexity for both problems. To show the efficiency of our implementations, we carry out some performance experiments and compare the results with those obtained by other classical algorithms.

quant-ph↗

arXiv2025

FTNILO: Explicit Multivariate Function Inversion, Optimization and Counting, Cryptography Weakness and Riemann Hypothesis Solution Equation with Tensor Networks

In this paper, we present a new formalism, the Field Tensor Network Integral Logical Operator (FTNILO), to obtain the explicit equation that returns the minimum, maximum, and zeros of a multivariable injective function, and an algorithm for non-injective ones. This method extends the MeLoCoToN algorithm for inversion and optimization problems with continuous variables, by using Field Tensor Networks. The fundamentals of the method are the conversion of the problem of minimization of $N$ continuous variables into a problem of maximization of a dependent functional of a single variable. It can also be adapted to determine other properties, such as the zeros of any function. For this purpose, we use an extension of the imaginary time evolution, the new method of continuous signals, and partial or total integration, depending on the case. In addition, we show a direct way to recover both the tensor networks and the MeLoCoToN from this formalism. We show some examples of application, such as the Riemann hypothesis resolution. We provide an explicit integral equation that gives the solution of the Riemann hypothesis, being that if it results in a zero value, it is correct; otherwise, it is wrong. This algorithm requires no deep mathematical knowledge and is based on simple mathematical properties.

math.OC↗

arXiv2025

Quantum Computing in Industrial Environments: Where Do We Stand and Where Are We Headed?

This article explores the current state and future prospects of quantum computing in industrial environments. Firstly, it describes three main paradigms in this field of knowledge: gate-based quantum computers, quantum annealers, and tensor networks. The article also examines specific industrial applications, such as bin packing, job shop scheduling, and route planning for robots and vehicles. These applications demonstrate the potential of quantum computing to solve complex problems in the industry. The article concludes by presenting a vision of the directions the field will take in the coming years, also discussing the current limitations of quantum technology. Despite these limitations, quantum computing is emerging as a powerful tool to address industrial challenges in the future.

quant-ph↗

arXiv2025

Introduction to QUDO, Tensor QUDO and HOBO formulations: Qudits, Equivalences, Knapsack Problem, Traveling Salesman Problem and Combinatorial Games

In this paper, we present a brief review and introduction to Quadratic Unconstrained D-ary Optimization (QUDO), Tensor Quadratic Unconstrained D-ary Optimization (T-QUDO) and Higher-Order Unconstrained Binary Optimization (HOBO) formulations for combinatorial optimization problems. We also show explicit encodings between these formulations and discuss their limitations. To help their understanding, we make some examples for the knapsack problem, traveling salesman problem and different combinatorial games. The games chosen to exemplify are: Hashiwokakero, N-Queens, Kakuro, Inshi no Heya, and Peg Solitaire. Although some of these games have already been formulated in a QUBO formulation, we are going to approach them with more general formulations, allowing their execution in new quantum or quantum-inspired optimization algorithms. This can be an easier way to introduce these more complicated formulations for harder problems.

cs.ET↗

arXiv2025

Fast Expectation Value Calculation Speedup of Quantum Approximate Optimization Algorithm: HoLCUs QAOA

In this paper, we present a new method for calculating expectation values of operators that can be expressed as a linear combination of unitary (LCU) operators. This method allows to perform this calculation in a single quantum circuit measuring a single qubit, which speeds up the computation process. This method is general for any quantum algorithm and is of particular interest in the acceleration of variational quantum algorithms, both in real devices and in simulations. We analyze its application to the parameter optimization process of the Quantum Approximate Optimization Algorithm (QAOA) and the case of having degenerate values in the matrix of the Ising problem. Finally, we apply it to several Quadratic Unconstrained Binary Optimization (QUBO) problems to analyze the speedup of the method in circuit simulators.

quant-ph↗

arXiv2025

A QUBO Formulation for the Generalized Takuzu/LinkedIn Tango Game

In this paper we present a QUBO formulation for the Takuzu game (or Binairo), for the most recent LinkedIn game, Tango, and for its generalizations. We optimize the number of variables needed to solve the combinatorial problem, making it suitable to be solved by quantum devices with fewer resources.

cs.OH↗

arXiv2025

Explicit Solution Equation for Every Combinatorial Problem via Tensor Networks: MeLoCoToN

In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint satisfaction and optimization, by obtaining its equivalent tensor network. This formulation only requires a basic knowledge of classical logical operators, at a first year level of any computer science degree. These equations are not necessarily computable in a reasonable time, nor do they allow to surpass the state of the art in computational complexity, but they allow to have a new perspective for the mathematical analysis of these problems. These equations computation can be approximated by different methods such as Matrix Product State compression. We also present the equations for numerous combinatorial problems. This work proves that, if there is a physical system capable of contracting in polynomial time the tensor networks presented, every NP-Hard problem can be solved in polynomial time.

cs.ET↗

arXiv2024

A QUBO Formulation for the Generalized LinkedIn Queens and Takuzu/Tango Game

In this paper, we present a QUBO formulation designed to solve a series of generalisations of the LinkedIn queens game, a version of the N-queens problem, for the Takuzu game (or Binairo), for the most recent LinkedIn game, Tango, and for its generalizations. We adapt this formulation for several particular cases of the problem, as Tents \& Trees, by trying to optimise the number of variables and interactions, improving the possibility of applying it on quantum hardware by means of Quantum Annealing or the Quantum Approximated Optimization Algorithm (QAOA). We also present two new types of problems, the Coloured Chess Piece Problem and the Max Chess Pieces Problem, with their corresponding QUBO formulations.

quant-ph↗

arXiv2024

Anomaly Detection from a Tensor Train Perspective

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.

cs.LG↗

arXiv2024

Private Delegated Quantum Computing for User-Level and Industry-Level Settings

We present a modular hierarchy of private delegated quantum computation protocols tailored to user-level and industry-level settings and parameterized by the quantum resources available to the client. For each protocol, we specify the client capabilities, delegated gate set, adversarial model, transcript leakage and resulting privacy claims. The hierarchy separates QOTP state privacy under declared leakage from leakage-dependent transcript-level angle ambiguity, compiler- and leakage-function-dependent structural privacy, and output privacy, clarifies when public Clifford operations can be evaluated on quantum-one-time-pad encrypted data by classical key updates, and identifies where non-Clifford privacy, non-collusion or additional primitives are required. The classical-client branch uses a persistent common-node, matching-hidden split-QOTP together with shuffled finite-grid $r$-share sign-randomized angle sharing to obtain leakage-relative state hiding under an explicit $\epsilon_{\mathrm{key}}$ key-hiding condition and transcript-level unlinkability under hidden-matching assumptions under an explicit non-total-collusion and leakage model. The angle-sharing primitives provide transcript ambiguity under explicit leakage assumptions, not universal blindness. The trap-based layer provides detection under stated assumptions, but it is not a stand-alone malicious-security proof.

quant-ph↗

arXiv2024

Quantum-inspired Techniques in Tensor Networks for Industrial Contexts

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.

quant-ph↗

arXiv2024

Técnicas Quantum-Inspired en Tensor Networks para Contextos Industriales

cs.CE↗

arXiv2023

Tensor-Network Formulation of the Traveling Salesman Problem and Variants

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 $\tau$ 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.

quant-ph↗

arXiv2023

Task Scheduling Optimization with Direct Constraints from a Tensor Network Perspective

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.

quant-ph↗