A new general quantum state verification protocol by the classical shadow method

Abstract

Verifying whether a quantum device produces a specific quantum state is a fundamental task in many applications of modern quantum technologies. In the conventional framework of quantum state verification, designing an optimal or efficient protocol for each type of state typically requires intricate, state-specific customization. Recently, Huang et al. (in: 2024 IEEE 65th annual symposium on foundations of computer science (FOCS), 2024) introduced a novel approach known as the shadow overlap protocol, which leverages classical shadows to efficiently verify multiple classes of quantum states simultaneously. In this work, we propose a new verification protocol that integrates key ideas from both the conventional framework and the shadow overlap protocol. To this end, we first reformulate the shadow overlap protocol using the formalism of hypothesis testing, which also underpins the conventional approach, and analyze the similarities and differences between the two. Our framework extends the capabilities of the shadow overlap protocol while addressing some of its limitations, yielding improved sample complexity and a more natural treatment of structured quantum states. We demonstrate the effectiveness of our protocol through applications to GHZ states and stabilizer states.