Filtering variational quantum algorithms for combinatorial optimization

Abstract Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use hardware efficiently. To make combinatorial optimization more efficient, we introduce filtering variational eigensolver which utilizes operators achieve faster and reliable convergence optimal solution. Additionally explore of causal cones reduce number qubits required on computer. Using random weighted MaxCut problems, numerically analyze our methods show that they perform better than original VQE algorithm approximate algorithm. We also demonstrate experimental feasibility Quantinuum trapped-ion processor powered by Honeywell.