Combinatorial optimization with quantum imaginary time evolution

Abstract

We use Quantum Imaginary Time Evolution (QITE) to solve polynomial unconstrained binary optimization (PUBO) problems. We show that a linear Ansatz yields good results for a wide range of PUBO problems, often outperforming standard classical methods, such as the Goemans-Williamson (GW) algorithm. We obtain numerical results for the Low Autocorrelation Binary Sequences (LABS) and weighted MaxCut combinatorial optimization problems, thus extending an earlier demonstration of successful application of QITE on MaxCut for unweighted graphs. We find the performance of QITE on the LABS problem with a separable Ansatz comparable with p=10 QAOA, and do not see a significant advantage with an entangling Ansatz. On weighted MaxCut, QITE with a separable Ansatz often outperforms the GW algorithm on graphs up to 150 vertices.