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