arXiv subjects

Jorge Martínez Martín

Publications and source records attributed to Jorge Martínez Martín.

4 recordsLinked to original sources

arXiv2026

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↗

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

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↗