Verifiable cloud-based variational quantum algorithms

Variational quantum algorithms (VQAs) have shown potential for quantum advantage with noisy intermediate-scale quantum (NISQ) devices for quantum machine learning (QML). However, given the high cost and limited availability of quantum resources, delegating VQAs via cloud networks is a more practical solution for clients with limited quantum capabilities. Recently, Shingu et al.[Physical Review A, 105, 022603 (2022)] proposed a variational secure cloud quantum computing protocol, utilizing ancilla-driven quantum computation (ADQC) for cloud-based VQAs with minimal quantum resource consumption. However, their protocol lacks verifiability, which exposes it to potential malicious behaviors by the server. Additionally, channel loss requires frequent re-delegation as the size of the delegated variational circuit grows, complicating verification due to increased circuit complexity. This paper introduces a new protocol to address these challenges and enhance both verifiability and tolerance to channel loss in cloud-based VQAs.