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arXiv:1407.1636 · Quantum Information and Computation

Impossibility of perfectly-secure one-round delegated quantum computing for classical client

Tomoyuki Morimae, Takeshi Koshiba

Published Mar 1, 2019• 15 citations
arXivHTMLPDF

Abstract

Blind quantum computing protocols enable a client, who can generate or measure single-qubit states, to delegate quantum computing to a remote quantum server protecting the client's privacy (i.e., input, output, and program). With current technologies, generations or measurements of single-qubit states are not too much burden for the client. In other words, secure delegated quantum computing is possible for ``almost classical" clients. However, is it possible for a ``completely classical" client? Here we consider a one-round perfectly-secure delegated quantum computing, and show that the protocol cannot satisfy both the correctness (i.e., the correct result is obtained when the server is honest) and the perfect blindness (i.e., the client's privacy is completely protected) simultaneously unless BQP is in NP. Since BQP is not believed to be in NP, the result suggests the impossibility of the one-round perfectly-secure delegated quantum computing.

DOI
10.26421/qic19.3-4-2

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•Jan 10, 2018•0 citations
Blind quantum computing protocols enable a client, who can generate or measure single-qubit states, to delegate quantum computing to a remote quantum server protecting the client's privacy (i.e., input, output, and program). With current technologies, generations or measurements of single-qubit states are not too much burden for the client. In other words, secure delegated quantum computing is possible for almost classical" clients. However, is it possible for a completely classical" client? Here we consider a one-round perfectly-secure delegated quantum computing, and show that the protocol cannot satisfy both the correctness (i.e., the correct result is obtained when the server is honest) and the perfect blindness (i.e., the client's privacy is completely protected) simultaneously unless BQP is in NP. Since BQP is not believed to be in NP, the result suggests the impossibility of the one-round perfectly-secure delegated quantum computing.
Blind quantum computing enables a client, who can only generate or measure single-qubit states, to delegate quantum computing to a remote quantum server in such a way that the input, output, and program are hidden from the server. It is an open problem whether a completely classical client can delegate quantum computing blindly (in the information theoretic sense). In this paper, we show that if a completely classical client can blindly delegate sampling of subuniversal models, such as the DQC1 model and the IQP model, then the polynomial-time hierarchy collapses to the third level. Our delegation protocol is the one where the client first sends a polynomial-length bit string to the server and then the server returns a single bit to the client. Generalizing the no-go result to more general setups is an open problem.
Blind quantum computation (BQC) protocol allows a client having partial quantum ability to delegate his quantum computation to a remote quantum server without leaking any information about the input, the output and the intended computation to the server. Several BQC protocols have been proposed, e.g., Li et al. in [1] proposed a triple-server BQC protocol and Xu et al. in [2] proposed a single-server BQC protocol. Though both papers claimed that their protocols can satisfy the requirement of privacy, this paper points out a security loophole in their protocols. With that the server can reveal the private information of the client.
Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness), and the correctness of the computation is verifiable by the client despite her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state, whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.
Suppose a large scale quantum computer becomes available over the Internet. Could we delegate universal quantum computations to this server, using only classical communication between client and server, in a way that is information-theoretically blind (i.e., the server learns nothing about the input apart from its size, with no cryptographic assumptions required)? In this paper we give strong indications that the answer is no. This contrasts with the situation where quantum communication between client and server is allowed --- where we know that such information-theoretically blind quantum computation is possible. It also contrasts with the case where cryptographic assumptions are allowed: there again, it is now known that there are quantum analogues of fully homomorphic encryption. In more detail, we observe that, if there exist information-theoretically secure classical schemes for performing universal quantum computations on encrypted data, then we get unlikely containments between complexity classes, such as BQP⊂NP/poly. Moreover, we prove that having such schemes for delegating quantum sampling problems, such as Boson Sampling, would lead to a collapse of the polynomial hierarchy. We then consider encryption schemes which allow one round of quantum communication and polynomially many rounds of classical communication, yielding a generalization of blind quantum computation. We give a complexity theoretic upper bound, namely QCMA/qpoly∩coQCMA/qpoly, on the types of functions that admit such a scheme. This upper bound then lets us show that, under plausible complexity assumptions, such a protocol is no more useful than classical schemes for delegating NP-hard problems to the server. Lastly, we comment on the implications of these results for the prospect of verifying a quantum computation through classical interaction with the server.
Abstract Blind quantum computation (BQC) allows a client without enough quantum technologies to delegate her quantum computation to a remote quantum server, while keeping her input, output and algorithm secure. In this paper, we propose a universal single-server and almost-classical-client BQC protocol. In this protocol, the client interfaces with only one server and the only ability of the client required is to get particles from the trusted center and forward them to the server. We present an analysis of this protocol and modify it to a universal single-server and fully-classical-client BQC protocol by improving the ability of the trusted center. Based on our protocols and recent works, a new ‘Cloud + Certificate Authority (CA)’ style is proposed for the BQC.
The characteristics of BQC is that it enables a client with less quantum abilities to delegate her quantum computation to a server with strong quantum computablities while keeping the client's privacy. In this article, we study single client-server BQC based on measurement which is verifiable. In detail, the verifiability is that the client Alice can obtain the correct measurement results if the server Bob is honest, while Bob does not get nothing of Alice's secret information if he is malicious. We construct a latticed state, composed of six-qubit cluster states and eight-qubit entangled states, to realize Alice's quantum computing. In this proposed protocol, the cilent Alice prepares and sends initial single-qubit states to Bob, where the initial states include useful qubits and trap qubits. And then Bob performs controlled-Z gate to produce the entanglement and returns them to Alice. Alice will send trap qubits and useful qubits to Bob randomly and Bob returns all measurement results to her. Alice makes a comparison for trap qubits between true results and Bob's results to check the honesty of Bob. In a word, the trap qubtis have two purposes: 1) confusing Bob to keep the blindness; 2)verifying the honesty of Bob and correctness of Bob's quantum computing. There has an important feature that Alice does not need to encrypt the computing angles by rπr\pirπ (r∈{0,1}\in\{0,1\}∈{0,1}), meanwhile the blindness and correctness can also be ensured. That is, Alice's computing results don't need to flipped since Bob is not impossible know anything about the quantum computation. Our work gives a better understanding for verifiable BQC based on measurement.