Michal Hajdušek, Carlos A. Pérez-Delgado, Joseph F. Fitzsimons
备注：
Shortly before submission of this preprint, the authors became aware of parallel and independent research by Gheorghiu, Kashefi and Wallden, which also addresses device-independent verifiable blind quantum computation, and appears simultaneously
As progress on experimental quantum processors continues to advance, the problem of verifying the correct operation of such devices is becoming a pressing concern. The recent discovery of protocols for verifying computation performed by entangled but non-communicating quantum processors holds the promise of certifying the correctness of arbitrary quantum computations in a fully device-independent manner. Unfortunately, all known schemes have prohibitive overhead, with resources scaling as extremely high degree polynomials in the number of gates constituting the computation. Here we present a novel approach based on a combination of verified blind quantum computation and Bell state self-testing. This approach has dramatically reduced overhead, with resources scaling as only $O(m^4\ln m)$ in the number of gates.
Blind quantum computation protocols allow a user with limited quantum technology to delegate an intractable computation to a quantum server while keeping the computation perfectly secret. Whereas in some protocols a user can verify that calculated outcomes are correct, a third party cannot do this, which allows a dishonest user or owner to benefit illegally. I propose a new blind quantum computation protocol with a new property called public verifiability, which enables any third party to assure that a party does not benefit from attempted deception.
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 in spite of 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-qu…
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 cl…
Quantum computing has considerable advantages in solving some problems over its classical counterpart. Currently various physical systems are developed to construct quantum computers but it is still challenging and the first use of quantum computers may adopt the cloud style. Blind quantum computing (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computation to remote quantum servers while keeping input, output, and even algorithm private. In this paper, we propose three multi-party verifiable blind quantum computing (VBQC) protocols with ident…
Verifiable blind quantum computing allows a client with poor quantum devices to delegate universal quantum computing to a remote quantum server in such a way that the client's privacy is protected and the honesty of the server is verified. In existing protocols, the client has to send single-qubit states to the server. These states might be decohered by the channel noise. Furthermore, the client hides some "trap" qubits in the server's register so that the client can detect the server's deviation. In reality, however, these trap qubits are disturbed by imperfect operations by the server, which…
We introduce a simple protocol for verifiable measurement-only blind quantum computing. Alice, a client, can perform only single-qubit measurements, whereas Bob, a server, can generate and store entangled many-qubit states. Bob generates copies of a graph state, which is a universal resource state for measurement-based quantum computing, and sends Alice each qubit of them one by one. Alice adaptively measures each qubit according to her program. If Bob is honest, he generates the correct graph state, and therefore Alice can obtain the correct computation result. Regarding the security, whateve…
We present a verifiable and blind protocol for assisted universal quantum computing on continuous-variable (CV) platforms. This protocol is highly experimentally-friendly to the client, as it only requires Gaussian-operation capabilities from the latter. Moreover, the server is not required 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…
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 Fitzsimons and Kashefi (2012) in the most general scenario. This includes the case where the purificati…
Experimental verifiable multi-client blind quantum computing on a Qline architecture
Dipartimento di Fisica - Sapienza Università di Roma（罗马大学物理系）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；VeriQloud；Laboratoire d’Informatique de Paris 6, CNRS, Sorbonne Université（巴黎第六大学计算机实验室，法国国家科学研究中心，索邦大学）
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. The authors, together with Broadbent, previously proposed…
We define the functionality of delegated pseudo-secret random qubit generator (PSRQG), where a classical client can instruct the preparation of a sequence of random qubits at some distant party. Their classical description is (computationally) unknown to any other party (including the distant party preparing them) but known to the client. We emphasize the unique feature that no quantum communication is required to implement PSRQG. This enables classical clients to perform a class of quantum communication protocols with only a public classical channel with a quantum server. A key such example i…
The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers. Our protocols have near-optimal complexity in terms of the total resources employed by the verifier and the honest provers, with the total number of operations of each party, including the number of entangled pairs of qubits required of the honest provers, scaling as $O(g\log g)$ for delegating a circuit of size $g$. This i…
Verifiable blind quantum computing: Comparative analysis and design considerations for client architectures
QuTech, Delft University of Technology（代尔夫特理工大学 QuTech）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学 卡弗里纳米科学研究所）；Quantum Computer Science, EEMCS, Delft University of Technology（代尔夫特理工大学 EEMCS 量子计算机科学）
Optimizing Resource Costs: A Practical Guide to Achieving Target Security in Verifiable Blind Quantum Computing
QuTech, Delft University of Technology（代尔夫特理工大学 QuTech）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学 卡弗里纳米科学研究所）；Quantum Computer Science, EEMCS, Delft University of Technology（代尔夫特理工大学 EEMCS 量子计算机科学）
Recent developments make 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 computing initiated by Fitzsimons and Kashefi. We present here a new const…
Blind quantum computation is a two-party protocol which involves a server Bob who has rich quantum computational resource and provides quantum computation service and a client Alice who wants to delegate her quantum computation to Bob without revealing her quantum algorithms and her input to (resp., output from) the algorithms. Since Bob may be truant and pretend to execute some computation, Alice wants to verify Bob's computation. Verifiable blind quantum computation enables Alice to check whether Bob is cheating or not. If Bob is cheating and claims his innocence, Alice can refute the denial…
With the development of delegated quantum computation, clients will want to ensure confidentiality of their data and algorithms, and the integrity of their computations. While protocols for blind and verifiable quantum computation exist, they suffer from high overheads and from over-sensitivity: When running on noisy devices, imperfections trigger the same detection mechanisms as malicious attacks, resulting in perpetually aborted computations. We introduce the first blind and verifiable protocol for delegating BQP computations to a powerful server with repetition as the only overhead. It is c…
Recent experimental achievements motivate an ever-growing interest from companies starting to feel the limitations of classical computing. Yet, in light of ongoing privacy scandals, the future availability of quantum computing through remotely accessible servers pose peculiar challenges: Clients with quantum-limited capabilities want their data and algorithms to remain hidden, while being able to verify that their computations are performed correctly. Research in blind and verifiable delegation of quantum computing attempts to address this question. However, available techniques suffer not onl…
The importance of being able to verify quantum computation delegated to remote servers increases with recent development of quantum technologies. In some of the proposed protocols for this task, a client delegates her quantum computation to non-communicating servers in multiple rounds of communication. In this work, we propose the first protocol where the client delegates her quantum computation to two servers in one-round of communication. Another advantage of our protocol is that it is conceptually simpler than previous protocols. The parameters of our protocol also make it possible to prove…
Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum serve…
A user who does not have a quantum computer but wants to perform quantum computations may delegate his computation to a quantum cloud server. In order that the delegation works, it must be assured that no evil server can obtain any important information on the computation. The blind protocol was proposed as a way for the user to protect his information from the unauthorized actions of the server. Among the blind protocols proposed thus far, a protocol with two servers sharing entanglement, while it does not require to a user any quantum resource, does not allow the servers to communicate even …
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 a concrete bounds fo…
This paper proposes a model of tripartite blind quantum computation (TBQC), in which three independent participants hold different resources and accomplish a computational task through cooperation. The three participants are called C,S,T separately, where C needs to compute on his private data, and T has the required quantum algorithm, and S provides sufficient quantum computational resources. Then two concrete TBQC protocols are constructed. The first protocol is designed based on Broadbent-Fitzsimons-Kashefi protocol, and it cannot prevent from collusive attack of two participants. Then base…
The question of whether a fully classical client can delegate a quantum computation to an untrusted quantum server while fully maintaining privacy (blindness) is one of the big open questions in quantum cryptography. Both yes and no answers have important practical and theoretical consequences, and the question seems genuinely hard. The state-of-the-art approaches to securely delegating quantum computation, without exception, rely on granting the client modest quantum powers, or on additional, non-communicating, quantum servers. In this work, we consider the single server setting, and push the…
Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek to marry these concepts for the purpose of securing computation rather than communication. These protocols address the task of securely delegating quantum computation to an untrusted device while maintaining the privacy, and in some instances the integrity, of the computation. We present a review of the progress to date in this emerging area.
Blind quantum computation is a secure delegated quantum computing protocol where Alice who does not have sufficient quantum technology at her disposal delegates her computation to Bob who has a fully-fledged quantum computer in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. Protocols of blind quantum computation have been proposed for several qubit measurement-based computation models, such as the graph state model, the Affleck-Kennedy-Lieb-Tasaki model, and the Raussendorf-Harrington-Goyal topological model. Here, we consider blind quantum computation fo…
Blindness is a desirable feature in delegated computation. In the classical setting, blind computations protect the data or even the program run by a server. In the quantum regime, blind computing may also enable testing computational or other quantum properties of the server system. Here we propose a scheme for universal blind quantum computation using a quantum simulator capable of emulating Heisenberg-like Hamiltonians. Our scheme is inspired by the central spin Hamiltonian in which a single spin controls dynamics of a number of bath spins. We show how, by manipulating this spin, a client t…
Blind quantum computation (BQC) allows a client with limited quantum power to delegate his quantum computational task to a powerful server and still keep his input, output, and algorithm private. There are mainly two kinds of models about BQC, namely circuit-based and measurement-based models. In addition, a hybrid model called ancilla-driven universal blind quantum computing (ADBQC) was proposed by combining the properties of both circuit-based and measurement-based models, where all unitary operations on the register qubits can be realized with the aid of single ancillae coupled to the regis…
Blind quantum computation is a new quantum secure protocol, which enables Alice who does not have enough quantum technology to delegate her computation to Bob who has a fully-fledged quantum power without revealing her input, output and algorithm. So far, blind quantum computation has been considered only for the circuit model and the measurement-based model. Here we consider the possibility and the limitation of blind quantum computation in the ancilla-driven model, which is a hybrid of the circuit and the measurement-based models.
Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation…
Because quantum computers are expensive, it is envisaged that individuals who want to utilize them would do so by delegating their calculations to someone who has a quantum computer. When quantum computer users delegate computations to quantum servers, they wish to keep information about their calculations hidden from the servers. The protocol of delegating a calculation while hiding information about the calculation from the server is called {\sl blind quantum computation protocol}. Prior research on single-server's blind quantum computation protocol required users to have quantum capabilitie…
Blind quantum computation (BQC) is a model in which a computation is performed on a server by a client such that the server is kept blind about the input, the algorithm, and the output of the computation. Here we layout a general framework for BQC which, unlike the previous BQC models, does not constructed on specific computational model. A main ingredient of our construction is gate teleportation. We demonstrate that our framework can be straightforwardly implemented on circuit-based models as well as measurement-based models of quantum computation. We illustrate our construction by showing t…
Blind quantum computation 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 blind quantum computation 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-clie…
Here we extend the concept of blind client-server quantum computation, in which a client with limited quantum power controls the execution of a quantum computation on a powerful server, without revealing any details of the computation. Our extension is to introduce a three-node setting in which an oracular quantum computation can be executed blindly. In this Blind Oracular Quantum Computation (BOQC), the oracle (Oscar) is another node, with limited power, who acts in cooperation with the client (Alice) to supply quantum information to the server so that the oracle part of the quantum computati…
We propose and analyze a novel interactive protocol for demonstrating quantum computational advantage, which is efficiently classically verifiable. Our protocol relies upon the cryptographic hardness of trapdoor claw-free functions (TCFs). Through a surprising connection to Bell's inequality, our protocol avoids the need for an adaptive hardcore bit, with essentially no increase in the quantum circuit complexity and no extra cryptographic assumptions. Crucially, this expands the set of compatible TCFs, and we propose two new constructions: one based upon the decisional Diffie-Hellman problem a…
Blind quantum computation (BQC) protocol allows a client having partially quantum ability to del- egate his quantum computation to a remote quantum server without leaking any information about the input, the output and the intended computation. Recently, many BQC protocols have been proposed with the intention to make the ability of client more classical. In this paper, we propose two BQC protocols, in which the client does not have to generate photons, but only has to perform either rotation or reorder on the received photons.
Simulation of Two-Qubit Grover Algorithm in MBQC with Universal Blind Quantum Computation
Electronics and Telecommunications Research Institute (ETRI)（电子电信研究所）；Cryptography Engineering Laboratory, Electronics and Telecommunications Research Institute (ETRI)（电子电信研究所密码工程实验室）
In the universal blind quantum computation problem, a client wants to make use of a single quantum server to evaluate $C|0\rangle$ where $C$ is an arbitrary quantum circuit while keeping $C$ secret. The client's goal is to use as few resources as possible. This problem, with a representative protocol by Broadbent, Fitzsimons and Kashefi [FOCS09, arXiv:0807.4154], has become fundamental to the study of quantum cryptography, not only because of its own importance, but also because it provides a testbed for new techniques that can be later applied to related problems (for example, quantum computa…
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 …
Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraints only hold in limited scenarios and show how to overcome it using a method based on iterated gate-teleportations. We present our results as a family of protocols, with varying degrees of computa…
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 …
Blind Quantum Computation (BQC) is a delegation computing protocol that allows a client to utilize a remote quantum server to implement desired quantum computations while keeping her inputs, outputs, and algorithms private. However, qubit errors during the quantum computation are important issues that need to be addressed. In this paper, we propose a fault-tolerant blind quantum computation protocol with quantum error-correcting codes to avoid the accumulation and propagation of qubit errors during the computational process. We further propose to apply the concatenated codes in the protocol to…
Blind delegation protocols allow a client to delegate a computation to a server so that the server learns nothing about the input to the computation apart from its size. For the specific case of quantum computation we know that blind delegation protocols can achieve information-theoretic security. In this paper we prove, provided certain complexity-theoretic conjectures are true, that the power of information-theoretically secure blind delegation protocols for quantum computation (ITS-BQC protocols) is in a number of ways constrained. In the first part of our paper we provide some indication t…
