Abstract
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 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. We also demonstrate the experimental feasibility of our algorithms on a Quantinuum trapped-ion quantum processor powered by Honeywell.
Highlights
Combinatorial optimization tackles problems of practical relevance [1]
Quantum Approximate Optimization Algorithm (QAOA) uses a specific ansatz circuit inspired by adiabatic quantum computation [17] and the Trotterization of the time evolution corresponding to quantum annealing [18]
We investigate the performance of Filtering Variational Quantum Eigensolver (VQE) (F-VQE) for various filtering operators and of HE-imaginary time evolution (ITE) using MaxCut problems on random 3-regular weighted graphs of different sizes
Summary
Combinatorial optimization tackles problems of practical relevance [1]. Applications include finding the shortest route via several locations for a delivery service, making optimal use of available storage space in logistics, and optimizing a manufacturing supply chain to increase the productivity of a factory. Variational quantum algorithms are a promising tool to get the most out of the current generation of gate-based quantum processors [2,3,4,5,6,7] These algorithms employ parameterized quantum circuits that can be tailored to hardware constraints such as qubit connectivities and gate fidelities. In this context, a common approach for combinatorial optimization encodes the optimal solution in the ground state of a classical multi-qubit Hamiltonian [8,9,10]. The repeated action of a filtering operator on a quantum state projects out high-energy eigenstates (corresponding to sub-optimal solutions of the combinatorial optimization problem) and increases the overlap with the ground state. In another publication [26] we analyse the performance of F-VQE in the context of the job shop scheduling problem
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