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

TL;DR

This paper introduces a quantum-inspired tensor network algorithm for solving various combinatorial optimization problems, demonstrating advantages over traditional solvers in multiple instances.

Contribution

It presents a novel tensor network approach based on MeLoCoToN methodology, including two methods for k-neighbors interactions and a new 'Waterfall' technique.

Findings

The tensor network algorithm outperforms quadratic optimization solvers in several problem instances.

Two approaches for k-neighbors interactions are developed: tensor contraction and matrix-vector multiplication.

The 'Waterfall' technique enhances sparse computation efficiency.

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.