Filtering variational quantum algorithms for combinatorial optimization

TL;DR

This paper introduces the Filtering Variational Quantum Eigensolver (F-VQE) that employs filtering operators and causal cones to enhance the efficiency and reliability of quantum algorithms for combinatorial optimization, with promising numerical and experimental results.

Contribution

The paper presents a novel F-VQE algorithm with filtering operators and causal cones, improving convergence and qubit efficiency over existing methods.

Findings

F-VQE outperforms original VQE and QAOA in numerical tests.

F-VQE demonstrates experimental feasibility on a trapped-ion quantum processor.

Filtering operators accelerate convergence to optimal solutions.

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 (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.