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arXiv:1708.06144 · Physical Review A

Classical multiparty computation using quantum resources

Marco Clementi, Anna Pappa, A. Eckstein, Ian A. Walmsley, Elham Kashefi, Stefanie Barz

Published Dec 18, 2017• 20 citations
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Abstract

In this work, we demonstrate a way to perform classical multiparty computing among parties with limited computational resources. Our method harnesses quantum resources to increase the computational power of the individual parties. We show how a set of clients restricted to linear classical processing are able to jointly compute a nonlinear multivariable function that lies beyond their individual capabilities. The clients are only allowed to perform classical xor gates and single-qubit gates on quantum states. We also examine the type of security that can be achieved in this limited setting. Finally, we provide a proof-of-concept implementation using photonic qubits that allows four clients to compute a specific example of a multiparty function, the pairwise and.

DOI
10.1103/physreva.96.062317

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In this work, we demonstrate a way to perform classical multiparty computing among parties with limited computational resources. Our method harnesses quantum resources to increase the computational power of the individual parties. We show how a set of clients restricted to linear classical processing are able to jointly compute a nonlinear multivariable function that lies beyond their individual capabilities. The clients are only allowed to perform classical xor gates and single-qubit gates on quantum states. We also examine the type of security that can be achieved in this limited setting. Finally, we provide a proof-of-concept implementation using photonic qubits that allows four clients to compute a specific example of a multiparty function, the pairwise and.
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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.
Secure multi-party computation (SMPC) protocols allow several parties that distrust each other to collectively compute a function on their inputs. In this paper, we introduce a protocol that lifts classical SMPC to quantum SMPC in a composably and statistically secure way, even for a single honest party. Unlike previous quantum SMPC protocols, our proposal only requires very limited quantum resources from all but one party; it suffices that the weak parties, i.e. the clients, are able to prepare single-qubit states in the X-Y plane. The novel quantum SMPC protocol is constructed in a naturally modular way, and relies on a new technique for quantum verification that is of independent interest. This verification technique requires the remote preparation of states only in a single plane of the Bloch sphere. In the course of proving the security of the new verification protocol, we also uncover a fundamental invariance that is inherent to measurement-based quantum computing.
A longstanding question is whether it is possible to delegate computational tasks securely---such that neither the computation nor the data is revealed to the server. Recently, both a classical and a quantum solution to this problem were found [C. Gentry, in Proceedings of the 41st Annual ACM Symposium on the Theory of Computing (Association for Computing Machinery, New York, 2009), pp. 167--178; A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual Symposium on Foundations of Computer Science (IEEE Computer Society, Los Alamitos, CA, 2009), pp. 517--526]. Here, we study the first step towards the interplay between classical and quantum approaches and show how coherence can be used as a tool for secure delegated classical computation. We show that a client with limited computational capacity---restricted to an XOR gate---can perform universal classical computation by manipulating information carriers that may occupy superpositions of two states. Using single photonic qubits or coherent light, we experimentally implement secure delegated classical computations between an independent client and a server, which are installed in two different laboratories and separated by 50m50\phantom{\rule{0.16em}{0ex}}\mathrm{m}50m. The server has access to the light sources and measurement devices, whereas the client may use only a restricted set of passive optical devices to manipulate the information-carrying light beams. Thus, our work highlights how minimal quantum and classical resources can be combined and exploited for classical computing.
We present a quantumly-enhanced protocol to achieve unconditionally secure delegated classical computation where the client and the server have both limited classical and quantum computing capacity. We prove the same task cannot be achieved using only classical protocols. This extends the work of Anders and Browne on the computational power of correlations to a security setting. Concretely, we present how a client with access to a non-universal classical gate such as a parity gate could achieve unconditionally secure delegated universal classical computation by exploiting minimal quantum gadgets. In particular, unlike the universal blind quantum computing protocols, the restriction of the task to classical computing removes the need for a full universal quantum machine on the side of the server and makes these new protocols readily implementable with the currently available quantum technology in the lab.
Abstract Secure multi-party computation (SMPC) protocols allow several parties distrusting each other to collectively compute a function on their inputs, without revealing the input values. In this paper, we introduce a protocol that lifts SMPC to its quantum counterpart—secure multi-party quantum computation (SMPQC) for classical inputs and outputs—in a composable and statistically secure way, even for a single honest party. The soundness error—the maximum cheating probability of malicious parties—is shown to be proportional to the inverse of a polynomial with respect to the number of rounds in the protocol, and can be further decreased to a negligible quantity for bounded-error quantum-polynomial-time computations. Unlike previous SMPQC protocols, our proposal only requires very limited quantum resources from all but one party. In addition, the protocol exhibits some noise robustness that can facilitate small-scale implementations with near-future technologies. The protocol is based on a new technique for quantum verification that requires only the collective remote preparation of quantum states in a single plane of the Bloch sphere. To demonstrate the ability of verifying the computation with such limited clients, we uncover and use a fundamental invariance that is inherent to measurement-based quantum computing.