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We present an algorithm for solving tridiagonal Quadratic UnconstrainedBinary Optimization (QUBO) problems and Quadratic Unconstrained DiscreteOptimization (QUDO) problems with one-neighbor interactions using thequantum-inspired technology of tensor networks. Our method is based on thesimulation of a quantum state to which we will apply an imaginary timeevolution and perform a series of partial traces to obtain the state of maximumamplitude, since it will be the optimal state. We will also deal with thedegenerate case and check the polynomial complexity of the algorithm.

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