A Quantum Approach to Stochastic Optimization in Insurance Underwriting

TL;DR

This paper introduces a quantum-classical hybrid method using QAOA circuits to solve stochastic chance-constrained knapsack problems, showing promising results on IBM hardware that could surpass classical methods.

Contribution

It presents a novel hybrid quantum-classical approach employing QAOA for stochastic optimization, with experimental validation on real quantum hardware.

Findings

Solutions indicate improvement over classical schemes.

Experiments used circuits with depths up to 177 and 150 qubits.

Demonstrates potential of quantum methods for complex stochastic problems.

Abstract

The presence of stochastic elements in combinatorial optimization problems makes them particularly challenging, as such problems quickly become intractable for classical computers even at relatively small sizes. In this work, we propose a novel quantum-classical hybrid scheme for solving a class of stochastic optimization problems known as chance-constrained knapsack problems, in which item weights follow probability distributions and constraints may be violated within a specified risk tolerance. Our method employs knapsack-specific QAOA-based circuits to generate samples which, when combined with a self-consistent classical recovery scheme introduced in this work, produce high-quality solutions. Experiments carried out on IBM Heron processors, using circuits with depths up to 177 and comprising 3443 gates acting on as many as 150 qubits, yield solutions that indicate improvement over classical optimization schemes. The proposed quantum-classical scheme paves the way to tackling such problems, with the potential to outperform approaches that rely solely on classical computation.