Quantum-inspired Tensor Network for QUBO, QUDO and Tensor QUDO Problems with k-neighbors
This addresses optimization problems in fields like logistics or scheduling, but it appears incremental as it builds on existing tensor network and quantum-inspired methods.
The authors tackled combinatorial optimization problems like QUBO, QUDO, and T-QUDO by developing a tensor network algorithm based on MeLoCoToN, which uses superposition and imaginary time evolution, and they introduced two approaches for k-neighbors interactions, showing advantages over a quadratic solver in some instances.
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.