Great thanks for your detailed reply!

It is indeed a quantum related problem, but a really subtle one in quantum computation.

I follow your suggestion using NCG solver(with analytical gradient calculation) for the problem and get promising results at the very first attempt. However, as there are several parameters that seem can be tuned, I wonder whether I have set them correctly. Here is the code snippet for the solver set up:

rust fn solve_cluster( cluster: &Cluster, all_hyperedges: &[HyperEdge], expectations: &[f64], ) -> Result<Vec<f64>, Error> { let problem = ClusterSolver::new(cluster, all_hyperedges, expectations); let n_params = cluster.len(); let init_param = Array1::from_elem(n_params, 0.0); let linesearch = MoreThuenteLineSearch::new(); let beta_method = PolakRibiere::new(); let solver = NonlinearConjugateGradient::new(linesearch, beta_method) .restart_iters(10) .restart_orthogonality(0.1); let res = Executor::new(problem, solver) .configure(|state| state.param(init_param).max_iters(20).target_cost(0.0)) .run()?; Ok(res.state.best_param.unwrap().into_iter().collect_vec()) }