Hybrid Quantum Algorithms integrating QAOA, Penalty Dephasing and Zeno Effect for Solving Binary Optimization Problems with Multiple Constraints

TL;DR

This paper introduces a hybrid quantum algorithm framework that combines QAOA, penalty dephasing, and the Zeno effect to efficiently solve large-scale binary optimization problems with multiple constraints, enhancing error handling and applicability.

Contribution

It proposes a novel hybrid quantum approach integrating Ising and non-Ising formulations with measurement-based constraint resolution techniques.

Findings

Effective handling of multiple constraints in quantum optimization.

Promising results on aircraft loading problem.

Flexible quantum circuit structures for different constraints.

Abstract

When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems involving multiple constraints. To address these challenges, this paper presents a hybrid framework that combines the use of standard Ising Hamiltonians to solve a subset of the constraints, while employing non-Ising formulations to represent and address the remaining constraints. The resolution of these non-Ising constraints is achieved through either penalty dephasing or the quantum Zeno effect. This innovative approach leads to a collection of quantum circuits with adaptable structures, depending on the chosen representation for each constraint. Furthermore, this paper introduces a novel technique that utilizes the quantum Zeno effect by frequently measuring the constraint flag, enabling the resolution of any optimization constraint. Theoretical properties of these algorithms are discussed, and their performance in addressing practical aircraft loading problems is highly promising, showcasing significant potential for a wide range of industrial applications.