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

2026-03-30

AI Summary

This work proposes a quantum-inspired tensor network algorithm based on the MeLoCoToN framework for combinatorial optimization problems involving k-local interactions, including QUBO, QUDO, and their higher-order tensor formulations. The approach integrates superposition-state initialization, imaginary-time evolution, and projective measurement, and introduces two efficient implementation strategies: one leveraging fourth-order tensor contraction and the other combining sparse matrix-vector multiplication with a novel “Waterfall” computational technique. As the first study to apply tensor networks to k-local QUBO/QUDO-type problems, the method demonstrates significant performance advantages over conventional quadratic optimization solvers across multiple benchmark instances, thereby validating its efficacy and computational superiority.

Abstract

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.

Problem

• QUBO
• QUDO
• Tensor Network
• k-neighbors
• Combinatorial Optimization

Innovation

• Tensor Network
• QUBO
• QUDO
• MeLoCoToN
• Waterfall