Verifiable multi-party delegated universal quantum computation against malicious participants

Delegated quantum computation (DQC) has emerged as a significant research focus to expedite the practical application of quantum advantage. Since substantial progress has been made in single-client DQC, extending these developments to multi-client settings naturally leads to the concept of multi-party delegated quantum computation (MPDQC). Existing MPDQC protocols predominantly rely on the prepare-and-send mode, while neglecting the receive-and-measure mode which is experimentally more practical. A key challenge hindering the adoption of the receive-and-measure mode in the multi-client scenario is the difficulty in verifying the local measurements of clients. In this paper, we address this obstacle and propose a verifiable MPDQC scheme tailored for multi-client settings. To enable federated computation among multiple clients, we construct a multi-client hypergraph state as the foundational resource state for MPDQC. Concurrently, we introduce a Pauli measurement verification protocol enabling the verification of client behavior within the multi-client framework, leveraging assistance from the quantum server. Building upon these advancements, we present a verifiable multiparty delegated universal quantum computation (MPDUQC) protocol and demonstrate its blindness and verifiability against malicious participants. Our work effectively bridges the gap for MPDQC protocols operating in the receive-and-measure paradigm.