Recent developments have brought the possibility of achieving scalable quantum networks and quantum devices closer. From the computational point of view these emerging technologies become relevant when they are no longer classically simulatable. Hence a pressing challenge is the construction of practical methods to verify the correctness of the outcome produced by universal or non-universal quantum devices. A promising approach that has been extensively explored is the scheme of verification via encryption through blind quantum computation. We present here a new construction that simplifies the required resources for any such verifiable protocol. We obtain an overhead that is linear in the size of the input (computation), while the security parameter remains independent of the size of the computation and can be made exponentially small (with a small extra cost). Furthermore our construction is generic and could be applied to any universal or non-universal scheme with a given underlying graph.
Finally a composable definition of @cite_23 is given in @cite_5 , while a limited computational model (one-pure-qubit) is examined in @cite_3 . Due to the generic nature of our construction these results would be applicable to our protocol as well.
@cite_5 @cite_3 @cite_23
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Delegating difficult computations to remote large computation facilities, with appropriate security guarantees, is a possible solution for the ever growing needs of personal computing power. For delegated computation protocols to be usable in a larger context – or simply to securely run two protocols in parallel – the security definitions need to be composable. Here, we define composable security for delegated quantum computation. We distinguish between protocols which provide only blindness – the computation is hidden from the server – and those that are also verifiable – the client can check that it has received the correct result. We show that the composable security definition capturing both these notions can be reduced to a combination of several distinct “trace distance type” criteria – which are, individually, non composable security definitions. While building a universal quantum computer remains challenging, devices of restricted power such as the so-called one pure qubit model have attracted considerable attention. An important step in the construction of these limited quantum computational devices is the understanding of whether the verification of the computation within these models could be also performed in the restricted scheme. Encoding via blindness (a cryptographic protocol for delegated computing) has proven successful for the verification of universal quantum computation with a restricted verifier. In this paper, we present the adaptation of this approach to the one pure qubit model, and present the first feasible scheme for the verification of delegated one pure qubit model of quantum computing. Blind quantum computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's input, output, and computation remain private. A desirable property for any BQC protocol is verification, whereby the client can verify with high probability whether the server has followed the instructions of the protocol or if there has been some deviation resulting in a corrupted output state. A verifiable BQC protocol can be viewed as an interactive proof system leading to consequences for complexity theory. We previously proposed [A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual Symposium on Foundations of Computer Science, Atlanta, 2009 (IEEE, Piscataway, 2009), p. 517] a universal and unconditionally secure BQC scheme where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. In this paper we extend that protocol with additional functionality allowing blind computational basis measurements, which we use to construct another verifiable BQC protocol based on a different class of resource states. We rigorously prove that the probability of failing to detect an incorrect output is exponentially small in a security parameter, while resource overhead remains polynomial in this parameter. This resource state allows entangling gates to be performed between arbitrary pairs of logical qubits with only constant overhead. This is a significant improvement on the original scheme, which required that all computations to be performed must first be put into a nearest-neighbor form, incurring linear overhead in the number of qubits. Such an improvement has important consequences for efficiency and fault-tolerance thresholds.