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International Journal of Intelligent Systems

Verifiable Multiparty Delegated Quantum Computation

Qin Li, Can Wang, Jiang Zhu, Lingling Xu, Zhiwei Sun

Published Jan 1, 2023• 5 citations
Publisher

Abstract

Multiparty delegated quantum computation (MDQC) allows multiple clients with limited quantum capability to jointly complete a quantum computational task with the aid of an untrusted quantum server. But in existing MDQC protocols, the verifiability that clients should verify whether the server executed the protocol correctly and gave correct results was not handled. Therefore, in this paper, we improve a typical MDQC protocol to enable clients to verify the correctness of computation by inserting trap qubits and develop a novel method to enforce clients to send qubits honestly while avoiding the positions of trap qubits being leaked to the server. The security and verifiability of the improved MDQC protocol are also analyzed. In addition, a specific example of the proposed verifiable MDQC protocol is given and simulated on IBM’s quantum platform.

DOI
10.1155/2023/2662685

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Multiparty delegated quantum computation (MDQC) allows multiple clients with limited quantum capability to jointly complete a quantum computational task with the aid of an untrusted quantum server. But in existing MDQC protocols, the verifiability that clients should verify whether the server executed the protocol correctly and gave correct results was not handled. Therefore, in this paper, we improve a typical MDQC protocol to enable clients to verify the correctness of computation by inserting trap qubits and develop a novel method to enforce clients to send qubits honestly while avoiding the positions of trap qubits being leaked to the server. The security and verifiability of the improved MDQC protocol are also analyzed. In addition, a specific example of the proposed verifiable MDQC protocol is given and simulated on IBM’s quantum platform.
In this paper, we propose a multiparty delegated quantum computing protocol for the completely classical clients. Our protocol is mainly based on the work of Cojocaru et al, in which they proposed a concrete protocol that can make a classical client instruct a quantum server to prepare a random qubit. We simplify their protocol by replacing the one-way functions with the one-way permutations that are post-quantum secure only. Then we extend this improved scheme to multiparty delegated quantum computation, where a group of classical clients can delegate their joint computation task to a distrusted quantum server.
Delegated quantum computation enables a client with limited quantum capabilities to outsource computations to a more powerful quantum server while preserving correctness and privacy. Verification is crucial in this setting to ensure that the untrusted quantum server performs the computation honestly and returns correct results. A common verification method is the quantum cut-and-choose technique. Inspired by classical verification methods for two-party computation, the client uses the majority of the delegated rounds to test the server's honesty, while keeping the remaining ones for the actual computation. Combining this technique with other methods, such as quantum error correction, could help achieve negligible cheating probabilities for the server; however, such methods can impose significant overheads making implementations unfeasible for the near-term future. In this work, we investigate whether cut-and-choose can yield efficient and secure verifiable quantum computation without additional costly techniques. We find that verifiable delegated quantum computation protocols relying solely on cut-and-choose techniques cannot be secure and efficient at the same time.
We construct a multi-Client verifiable blind delegated quantum computing (VBDQC) protocol in which M classical Verifier Clients jointly delegate a public quantum circuit acting on their combined private inputs to two quantum-capable Provers sharing entanglement but having no direct communication channel. We begin by modifying the single-Client, entanglement-based CGJV Verifier-on-a-Leash protocol. We then prove simulator-based blind verifiability for the modified protocol using the abstract/constructive cryptography framework. We adapt the DFPR upward-reduction chain to the two-Prover setting, constructing a no-direct-communication simulator architecture. We then extend the CGJV protocol to M Clients using classical multiparty computation techniques, preserving the single-Client guarantees of completeness, soundness, and blindness while additionally guaranteeing input privacy between Clients. Security is analyzed under a threat model that allows a subset of Clients to collude with one but not both of the Provers, which do not communicate even after the protocol execution.
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.
In blind quantum computation (BQC), a client with weak quantum computation capabilities is allowed to delegate its quantum computation tasks to a server with powerful quantum computation capabilities, and the inputs, algorithms and outputs of the quantum computation are confidential to the server. Verifiability refers to the ability of the client to verify with a certain probability whether the server has executed the protocol correctly and can be realized by introducing trap qubits into the computation graph state to detect server deception. The existing verifiable universal BQC protocols are analyzed and compared in detail. The XTH protocol (proposed by Xu Q S, Tan X Q, Huang R in 2020), a recent improvement protocol of verifiable universal BQC, uses a sandglass-like graph state to further decrease resource expenditure and enhance verification capability. However, the XTH protocol has two shortcomings: limitations in the coloring scheme and a high probability of accepting an incorrect computation result. In this paper, we present an improved version of the XTH protocol, which revises the limitations of the original coloring scheme and further improves the verification ability. The analysis demonstrates that the resource expenditure is the same as for the XTH protocol, while the probability of accepting the wrong computation result is reduced from the original minimum (0.866) d* to (0.819) d*, where d* is the number of repeated executions of the protocol.
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.