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Verifiable multi-party delegated universal quantum computation against malicious participants

Zimeng Yuan, Jing Li, Chun Long, Fan Yang, Yuhao Fu, X. Pan

Published Feb 5, 2026• 0 citations
Publisher

Abstract

Abstract 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.

DOI
10.21203/rs.3.rs-7062010/v1

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Abstract 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.
Multi-Party Quantum Computation (MPQC) has attracted a lot of attention as a potential killer-app for quantum networks through it's ability to preserve privacy and integrity of the highly valuable computations they would enable. Contributing to the latest challenges in this field, we present a composable protocol achieving blindness and verifiability even in the case of a single honest client. The security of our protocol is reduced, in an information-theoretically secure way, to that of a classical composable Secure Multi-Party Computation (SMPC) used to coordinate the various parties. Our scheme thus provides a statistically secure upgrade of such classical scheme to a quantum one with the same level of security. In addition, (i) the clients can delegate their computation to a powerful fully fault-tolerant server and only need to perform single qubit operations to unlock the full potential of multi-party quantum computation; (ii) the amount of quantum communication with the server is reduced to sending quantum states at the beginning of the computation and receiving the output states at the end, which is optimal and removes the need for interactive quantum communication; and (iii) it has a low constant multiplicative qubit overhead compared to the single-client delegated protocol it is built upon. The main technical ingredient of our paper is the bootstraping of the MPQC construction by Double Blind Quantum Computation, a new composable resource for blind multiparty quantum computation, that demonstrates the surprising fact that the full protocol does not require verifiability of all components to achieve security.
ABSTRACT With the advent of delegated quantum computing as a service, verifying the integrity of quantum computations is becoming a question of great importance. Existing information‐theoretically Secure Delegated Quantum Computing (SDQC) protocols require the client to possess the ability to perform either trusted state preparations or measurements. Whether it is possible to verify universal quantum computations with information‐theoretic security without trusted preparations or measurements was an open question so far. In this paper, we settle this question in the affirmative by presenting a modular, composable, and efficient way to turn known verification schemes into protocols that rely only on trusted gates. Our first contribution is an extremely lightweight reduction of the problem of quantum verification for to the trusted application of single‐qubit rotations around the axis and bit flips. The second construction presented in this work shows that it is possible to information‐theoretically verify arbitrary quantum computations without trusted preparations or measurements if the verifier can perform two‐qubit gates on a register whose size is logarithmic in the security parameter. Our third contribution extends these two results to the multi‐party setting in which multiple mutually distrustful clients delegate a joint computation to a potentially malicious server.
Delegated quantum computing (DQC) allows clients with low quantum capabilities to outsource computations to a server hosting a quantum computer. This process is often envisioned within the measurement-based quantum computing framework, as it naturally facilitates blindness of inputs and computation. Hence, the overall process of setting up and conducting the computation encompasses a sequence of three stages: preparing the qubits, entangling the qubits to obtain the resource state, and measuring the qubits to run the computation. There are two primary approaches to distributing these stages between the client and the server that impose different constraints on cryptographic techniques and experimental implementations. In the prepare-and-send setting, the client prepares the qubits and sends them to the server, while in the receive-and-measure setting, the client receives the qubits from the server and measures them. Although these settings have been extensively studied independently, their interrelation and whether setting-dependent theoretical constraints are inevitable remain unclear. By implementing the key components of most DQC protocols in the respective missing setting, we provide a method to build prospective protocols in both settings simultaneously and to translate existing protocols from one setting into the other.
Delegated quantum computing (DQC) enables limited clients to perform operations that are outside their capabilities remotely on a quantum server. Protocols for DQC are usually set up in the measurement-based quantum computation framework, as this allows for a natural separation of the different parts of the computation between the client and the server. The existing protocols achieve several desired properties, including the security of inputs, the blindness of computation and its verifiability, and have also recently been extended to the multiparty setting. Two approaches are followed in DQC that demand completely different operations on the clients' side. In one, the clients are able to prepare quantum states, in the other, the clients are able to measure them. In this work, we provide a novel stringent definition of the equivalence of protocols and show that these distinct DQC settings are, in fact, equivalent in this sense. We use the abstract cryptography framework to prove our claims and provide a novel technique that enables changing from one setting to the other. In this way, we demonstrate that both approaches can be used to perform tasks with the same properties. I.e., using our proposed techniques, we can always translate from one setting to the other. We finally use our results to propose a hybrid-client model for DQC.
Blind quantum computation (BQC) provides a secure framework for clients to delegate quantum computations to servers without revealing their private information. Among BQC protocols, those built on iterated gate teleportation (IGTBQC) have demonstrated promising potential in overcoming the constraints imposed by the no-programming theorem and significantly reducing communication overhead. However, existing IGTBQC protocols lack mechanisms for clients to verify the correctness of computation results and deal with only one type of clients capable of preparing qubits. To address these limitations, we first extend the current IGTBQC protocol to be a verifiable one and then propose another verifiable IGTBQC protocol tailored for a different type of clients with the capability of measuring single-qubit states. Furthermore, both protocols are shown to satisfy blindness and verification simultaneously in a relatively formal way. Our results not only broaden the applicability to a wider range of clients but also enhance the practicality of delegated quantum computation.
Blind quantum computation (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computational tasks to remote quantum servers while keeping their own data private. In this paper, we first propose three multi-party verifiable blind quantum computation (MPVBQC) protocols, each of which can handle one type of clients with certain simple quantum capabilities such as making single-qubit measurements, preparing single qubits, or performing a few single-qubit gates. Then a flexible and hybrid MPVBQC framework for multi-type clients in quantum networks is given by combining the three proposed MPVBQC protocols. It simultaneously allows at least three types of clients in quantum networks to achieve BQC depending on their own quantum devices. Furthermore, all the proposed protocols can achieve identity authentication, resist both insider and outsider attacks, and be verifiable which means that the clients can verify the correctness of their computational results.