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arXiv:1306.2724 · Physical Review Letters

Efficient Universal Blind Quantum Computation

Vittorio Giovannetti, Lorenzo Maccone, Tomoyuki Morimae, Terry Rudolph

Published Dec 3, 2013• 87 citations
arXivHTMLPDF

Abstract

We give a cheat sensitive protocol for blind universal quantum computation that is efficient in terms of computational and communication resources: it allows one party to perform an arbitrary computation on a second party's quantum computer without revealing either which computation is performed, or its input and output. The first party's computational capabilities can be extremely limited: she must only be able to create and measure single-qubit superposition states. The second party is not required to use measurement-based quantum computation. The protocol requires the (optimal) exchange of O(Jlog2(N)) single-qubit states, where J is the computational depth and N is the number of qubits needed for the computation.

DOI
10.1103/physrevlett.111.230501

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We give a cheat sensitive protocol for blind universal quantum computation that is efficient in terms of computational and communication resources: it allows one party to perform an arbitrary computation on a second party's quantum computer without revealing either which computation is performed, or its input and output. The first party's computational capabilities can be extremely limited: she must only be able to create and measure single-qubit superposition states. The second party is not required to use measurement-based quantum computation. The protocol requires the (optimal) exchange of O(Jlog2(N)) single-qubit states, where J is the computational depth and N is the number of qubits needed for the 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.
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.
Blind quantum computation allows a client with limited quantum capabilities to interact with a remote quantum computer to perform an arbitrary quantum computation, while keeping the description of that computation hidden from the remote quantum computer. While a number of protocols have been proposed in recent years, little is currently understood about the resources necessary to accomplish the task. Here, we present general techniques for upper and lower bounding the quantum communication necessary to perform blind quantum computation, and use these techniques to establish concrete bounds for common choices of the client's quantum capabilities. Our results show that the universal blind quantum computation protocol of Broadbent, Fitzsimons, and Kashefi, comes within a factor of 8/3 of optimal when the client is restricted to preparing single qubits. However, we describe a generalization of this protocol which requires exponentially less quantum communication when the client has a more sophisticated device.
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.
Abstract Blind quantum computation (BQC) protocols enable quantum algorithms to be executed on third-party quantum agents while keeping the data and algorithm confidential. The previous proposals for measurement-based BQC require preparing a highly entangled cluster state. In this paper, we show that such a requirement is not necessary. Our protocol only requires pre-shared Bell pairs between delegated quantum agents, and there is no requirement for any classical or quantum information exchange between agents during the execution. Our proposal requires fewer quantum resources than previous proposals by eliminating the need for a universal cluster state.
Universal blind quantum computation allows a client who has limited quantum abilities to delegate his or her private computation to an untrusted quantum server. The first universal blind quantum computation protocol was proposed by Broadbent, Fitzsimons, and Kashefi. In their work the computation resource is the so-called brickwork state, which can be constructed by a number of specific single qubits. The number of single qubits is in theory linearly related to the size of the quantum circuit. However, due to the fixed structure of the brickwork states, the actual number of qubits is usually far more than the linear size. In this work we mainly construct three improved brickwork states whose structures are no longer fixed, thus they can efficiently reduce the client's qubit consumption. Using those improved brickwork states we propose a class of efficient universal blind quantum computation protocols. In our basic protocol, to implement a single-qubit basic gate the client needs to prepare only two ancillary qubits, while in the original protocol it will consume four ancillary qubits. Making use of our improved brickwork states the qubit consumption of implementing a nonadjacent two-qubit gate such as a control-XXX gate can be sharply reduced.