Robustness and device independence of verifiable blind quantum computing

Abstract

Recent advances in theoretical and experimental quantum computing bring us closer to scalable quantum computing devices. This makes the need for protocols that verify the correct functionality of quantum operations timely and has led to the field of quantum verification. In this paper we address key challenges to make quantum verification protocols applicable to experimental implementations. We prove the robustness of the single server verifiable universal blind quantum computing protocol of Kashefi (2012 arXiv:1203.5217) in the most general scenario. This includes the case where the purification of the deviated input state is in the hands of an adversarial server. The proved robustness property allows the composition of this protocol with a device-independent state tomography protocol that we give, which is based on the rigidity of CHSH games as proposed by Reichardt et al (2013 Nature 496 456-60). The resulting composite protocol has lower round complexity for the verification of entangled quantum servers with a classical verifier and, as we show, can be made fault tolerant.The approaches that have been so far successful are those based on interactive proof systems [6,7], where a trusted, computationally limited verifier (also known as client, in a cryptographic setting) exchanges messages with an untrusted, powerful quantum prover, or multiple provers (also known as servers). The verifier attempts to certify that, with high probability, the provers are performing the correct quantum operations. Because we are dealing with a new form of computation, the verification protocols, while based on established techniques are fundamentally different from their classical counterparts. A number of quantum verification protocols have been developed, for different functionalities of devices and using a variety of different strategies to achieve verification [1,2,[8][9][10][11][12][13][14][15][16][17]. The assumptions made depend on the specific target and desired properties of the protocol. For example, if the emphasis is on creating an immediate practical implementation, then this should be reflected in the technological requirements leading to a testable application with current technology [17]. Alternatively, if the motivation is to prove a theoretical result, we may relax some requirements such as efficient scaling [2]. An important open problem in the field of quantum verification, is whether a scheme with a fully classical verifier is possible [18,19]. We know, however, that verification is possible in the following two scenarios.(1)A verifier with minimal quantum capacity (ability to prepare random single qubits) and a single quantum prover [1]. This is the Fitzsimons and Kashefi (FK) protocol.(2)A fully classical verifier and two non-communicating quantum provers that share entanglement [20]. This is the Reichardt, Unger and Vazirani (RUV) protocol.One of our objectives is to obtain a device-independent (allowing untrusted quantum devices) version of the FK protocol, by composing it with the RUV protocol.Here we ...

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

“…This follows from the rigidity result of theorem 5. The result is analogous to that of [9,10] where the rigidity of CHSH games is used in the same fashion. All of this is encapsulated in protocol 1.…”

“…Instead, it is known that if the verifier has some minimal quantum capabilities, he is able to verify the prover's computation [32,54]. Alternatively, if there are multiple non-communicating provers sharing entanglement it is possible to do verification with a fully classical verifier [9,10,12]. It should be noted that in certain cases not all the provers are quantum computers.…”

“…In particular, the existence of non-local correlations, apart from revealing a counter intuitive feature of nature, has led to the development of device-independent protocols for quantum key distribution (QKD), quantum random number generation (QRNG) and verified delegated quantum computation (VDQC) [3,[9][10][11][12][13][14][15][16]. In these applications two parties, Alice and Bob, do not trust their devices throughout the run of the protocol.…”

“…Moreover, approaches to QKD and QRNG rely on using a bound on the correlations of the parties' devices in order to derive a bound for a quantity of interest, such as key rate, mutual information, entropy etc [15,[27][28][29][30][31]. In contrast to this, existing protocols for device-independent VDQC use the bound on correlations to recover the underlying quantum state used in the protocol, as well as the operations being performed on this quantum state [9][10][11][12]. This allows for the correctness certification (referred to here as verification) of an arbitrary universal quantum computation strictly from the non-local correlations.…”

“…However, in general, it is necessary to play a large number of games in order to certify few Bell states. For this reason the existing device-independent VDQC protocols have impractically large communication complexity [9,10,12].…”