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arXiv:1806.09137 · Physical Review A

Client-friendly continuous-variable blind and verifiable quantum computing

Nana Liu, Tommaso F. Demarie, Si-Hui Tan, Leandro Aolita, Joseph F. Fitzsimons

Published Dec 5, 2019• 11 citations
arXivHTMLPDF

Abstract

We present a verifiable and blind protocol for assisted universal quantum computing on continuous-variable (CV) platforms. This protocol is experimentally friendly to the client, as it only requires Gaussian-operation capabilities from the latter. Moreover, the server does not require universal quantum-computational power either, its only function being to supply the client with copies of a single-mode non-Gaussian state. Universality is attained based on state injection of the server's non-Gaussian supplies. The protocol is automatically blind because the non-Gaussian resource requested to the server is always the same, regardless of the specific computation. Verification, in turn, is possible thanks to an efficient non-Gaussian state fidelity test where we assume identical state preparation by the server. It is based on Gaussian measurements by the client on the injected states, which is potentially interesting on its own. The division of quantum hardware between client and server assumed here is in agreement with the experimental constraints expected in realistic schemes for CV cloud quantum computing.

DOI
10.1103/physreva.100.062309

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We present a verifiable and blind protocol for assisted universal quantum computing on continuous-variable (CV) platforms. This protocol is experimentally friendly to the client, as it only requires Gaussian-operation capabilities from the latter. Moreover, the server does not require universal quantum-computational power either, its only function being to supply the client with copies of a single-mode non-Gaussian state. Universality is attained based on state injection of the server's non-Gaussian supplies. The protocol is automatically blind because the non-Gaussian resource requested to the server is always the same, regardless of the specific computation. Verification, in turn, is possible thanks to an efficient non-Gaussian state fidelity test where we assume identical state preparation by the server. It is based on Gaussian measurements by the client on the injected states, which is potentially interesting on its own. The division of quantum hardware between client and server assumed here is in agreement with the experimental constraints expected in realistic schemes for CV cloud quantum computing.
Limitations due to high costs and technological requirements will require users to access the first quantum processors through the cloud. Delegating a computation, however, raises privacy issues about the clients' data and poses questions about the verifiability of computations in high complexity regimes. These concerns have inspired a plethora of blind and verifiable quantum computation protocols, which allow a client with limited quantum capabilities to delegate a quantum computation to a remote server while hiding her data and preserving the integrity of the computation. The majority of these protocols are constrained to discrete quantum systems, but quantum information can also be processed by continuous-variable architectures. These offer a competitive alternative to their discrete-variable counterparts for numerous practical benefits: They rely on well-established quantum optical techniques, allow for the generation of very large optical resource states, offer higher detection efficiencies, and can be integrated into existing optical-fibre networks, all of which are highly desirable features for cloud quantum computing. In this work we fill this gap by presenting a blind and verifiable quantum computing protocol tailored to the unique features of continuous-variable systems. One such feature is the experimental accessibility of Gaussian operations. Our protocol is then based on the delegation of the experimentally challenging non-Gaussian operations. In this sense, it is experimentally friendly to the client, who only needs to perform Gaussian operations. Furthermore, unlike previous schemes, this protocol does not require repeated interactions between the client and server because it only involves the server sending the client non-Gaussian states. We prove universality and blindness using standard techniques, and we introduce an efficient fidelity test - based on homodyne detection - that allows the client to verify the correctness of the computation. This test is interesting in its own right because it could be employed in the context of state-certification of optical systems. The division of quantum hardware between client and server assumed here is typical of the experimental constraints expected in realistic, commercially useful schemes for continuous-variable cloud quantum computing. As such, we believe our protocol constitutes a significant advance towards their actual realisation.
We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational power or memory. The client only needs to be able to prepare single qubits randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, the client and server use two-way classical communication which enables the client to drive the computation, giving single-qubit measurement instructions to the server, depending on previous measurement outcomes. Our protocol works for inputs and outputs that are either classical or quantum. We give an authentication protocol that allows the client to detect an interfering server; our scheme can also be made fault-tolerant. We also generalize our result to the setting of a purely classical client who communicates classically with two non-communicating entangled servers, in order to perform a blind quantum computation. By incorporating the authentication protocol, we show that any problem in BQP has an entangled two-prover interactive proof with a purely classical verifier. Our protocol is the first universal scheme which detects a cheating server, as well as the first protocol which does not require any quantum computation whatsoever on the client's side. The novelty of our approach is in using the unique features of measurement-based quantum computing which allows us to clearly distinguish between the quantum and classical aspects of a quantum computation.
We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational power or memory. The client only needs to be able to prepare single qubits randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, the client and server use two-way classical communication which enables the client to drive the computation, giving single-qubit measurement instructions to the server, depending on previous measurement outcomes. Our protocol works for inputs and outputs that are either classical or quantum. We give an authentication protocol that allows the client to detect an interfering server; our scheme can also be made fault-tolerant. We also generalize our result to the setting of a purely classical client who communicates classically with two non-communicating entangled servers, in order to perform a blind quantum computation. By incorporating the authentication protocol, we show that any problem in BQP has an entangled two-prover interactive proof with a purely classical verifier. Our protocol is the first universal scheme which detects a cheating server, as well as the first protocol which does not require any quantum computation whatsoever on the client's side. The novelty of our approach is in using the unique features of measurement-based quantum computing which allows us to clearly distinguish between the quantum and classical aspects of a quantum computation.
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.
In the field of single-server blind quantum computation (BQC), a major focus is to make the client as classical as possible. To achieve this goal, we propose two single-server BQC protocols to achieve verifiable universal quantum computation. In these two protocols, the client only needs to perform either the gate T (in the first protocol) or the gates H and X (in the second protocol). With assistance from a single server, the client can utilize his quantum capabilities to generate some single-qubit states while keeping the actual state of these qubits confidential from others. By using these single-qubit states, the verifiable universal quantum computation can be achieved.
Blind quantum computing enables a client, who does not have enough quantum technologies, to delegate her quantum computing to a remote quantum server in such a way that her privacy is protected against the server. Some blind quantum computing protocols can be made verifiable, which means that the client can check the correctness of server's quantum computing. Can any blind protocol always be made verifiable? In this paper, we answer to the open problem affirmatively. We propose a plug-in that makes any universal blind quantum computing protocol automatically verifiable. The idea is that the client blindly generates Feynman-Kitaev history states corresponding to the quantum circuit that solves client's problem and its complement circuit. The client can learn the solution of the problem and verify its correctness at the same time by measuring energies of local Hamiltonians on these states. Measuring energies of local Hamiltonians can be done with only single qubit measurements of Pauli operators.