Polynomial-time Solver of Tridiagonal QUBO, QUDO and Tensor QUDO problems with Tensor Networks

Abstract

We present a quantum-inspired tensor network algorithm for solving tridiagonal Quadratic Unconstrained Binary Optimization (QUBO) problems and quadratic unconstrained discrete optimization (QUDO) problems. We also solve the more general Tensor quadratic unconstrained discrete optimization (T-QUDO) problems with one-neighbor interactions in a lineal chain. This method provides an exact and explicit equation for these problems. Our algorithms are based on the simulation of a state that undergoes imaginary time evolution and a Half partial trace. In addition, we address the degenerate case and evaluate the polynomial complexity of the algorithm, also providing a parallelized version. We implemented and tested them with other well-known classical algorithms and observed an improvement in the quality of the results. The performance of the proposed algorithms is compared with the Google OR-TOOLS and dimod solvers, improving their results.