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Classical Analysis of Quantum Computation

Kentaro Honda

Published Mar 24, 2016• 0 citations
Publisher

Abstract

Quantum computation is based on quantum physics and different from classical computation based on classical physics.It has non-classical characteristics such as quantum superposition principle, uncertainty principle, and no-cloning theorem and has been mainly studied by original methodology.However, it does not mean we cannot investigate quantum computation using traditional methods that have been studied in non-quantum area.We believe that quite a lot of methods are useful to investigate quantum computation and it is important to find such methods.When they are found, they will accelerate the research of quantum computation using the knowledge about them.Moreover, due to their classical nature, they will naturally help us to analyse quantum computation using classical computers.In order to support the idea, we show two classical methodologies, abstract interpretation and classical public-key cryptography, enhance analysis in two topics of quantum computation, entanglement in quantum programming languages and blind quantum computation protocols.The behaviour of entangled quantum system is counterintuitive.Therefore, it is important to know how entangled states are in quantum programs without executing them.In order to statistically analyse the problem, it was proposed to apply the abstract interpretation technique to the analysis.However, the proposed method does not store information about entangled states and ignores the fact that an operator on multiple qubits may undo entanglements, and hence the method only gives a rough approximation.We combine the method with the stabiliser formalism.We show abstract interpretation can be used to efficiently analyse the existence of entanglement in quantum programs with higher precision.Blind quantum computation protocols give users having no powerful quantum devices a method to delegate their quantum computation to remote quantum servers without leaking any crucial information about their computation.Some protocols enable users to verify whether the quantum servers honestly do the delegated computation, but no protocols give third parties ways to analyse the computation.We propose a new blind quantum computation protocol using a classical public-key encryption scheme.Our protocol is based on an existing protocol, but third parties, who have only classical computers and check the classical message between users and quantum servers, can analyse the computation and verify whether users obtain the correct outcomes or not.These results show classical methodology, which achieves a development outside the area of quantum computation, may be useful for investigation of quantum computation.

DOI
10.15083/00073984

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Quantum computation is based on quantum physics and different from classical computation based on classical physics.It has non-classical characteristics such as quantum superposition principle, uncertainty principle, and no-cloning theorem and has been mainly studied by original methodology.However, it does not mean we cannot investigate quantum computation using traditional methods that have been studied in non-quantum area.We believe that quite a lot of methods are useful to investigate quantum computation and it is important to find such methods.When they are found, they will accelerate the research of quantum computation using the knowledge about them.Moreover, due to their classical nature, they will naturally help us to analyse quantum computation using classical computers.In order to support the idea, we show two classical methodologies, abstract interpretation and classical public-key cryptography, enhance analysis in two topics of quantum computation, entanglement in quantum programming languages and blind quantum computation protocols.The behaviour of entangled quantum system is counterintuitive.Therefore, it is important to know how entangled states are in quantum programs without executing them.In order to statistically analyse the problem, it was proposed to apply the abstract interpretation technique to the analysis.However, the proposed method does not store information about entangled states and ignores the fact that an operator on multiple qubits may undo entanglements, and hence the method only gives a rough approximation.We combine the method with the stabiliser formalism.We show abstract interpretation can be used to efficiently analyse the existence of entanglement in quantum programs with higher precision.Blind quantum computation protocols give users having no powerful quantum devices a method to delegate their quantum computation to remote quantum servers without leaking any crucial information about their computation.Some protocols enable users to verify whether the quantum servers honestly do the delegated computation, but no protocols give third parties ways to analyse the computation.We propose a new blind quantum computation protocol using a classical public-key encryption scheme.Our protocol is based on an existing protocol, but third parties, who have only classical computers and check the classical message between users and quantum servers, can analyse the computation and verify whether users obtain the correct outcomes or not.These results show classical methodology, which achieves a development outside the area of quantum computation, may be useful for investigation of quantum computation.
Suppose a large scale quantum computer becomes available over the Internet. Could we delegate universal quantum computations to this server, using only classical communication between client and server, in a way that is information-theoretically blind (i.e., the server learns nothing about the input apart from its size, with no cryptographic assumptions required)? In this paper we give strong indications that the answer is no. This contrasts with the situation where quantum communication between client and server is allowed --- where we know that such information-theoretically blind quantum computation is possible. It also contrasts with the case where cryptographic assumptions are allowed: there again, it is now known that there are quantum analogues of fully homomorphic encryption. In more detail, we observe that, if there exist information-theoretically secure classical schemes for performing universal quantum computations on encrypted data, then we get unlikely containments between complexity classes, such as BQP⊂NP/poly. Moreover, we prove that having such schemes for delegating quantum sampling problems, such as Boson Sampling, would lead to a collapse of the polynomial hierarchy. We then consider encryption schemes which allow one round of quantum communication and polynomially many rounds of classical communication, yielding a generalization of blind quantum computation. We give a complexity theoretic upper bound, namely QCMA/qpoly∩coQCMA/qpoly, on the types of functions that admit such a scheme. This upper bound then lets us show that, under plausible complexity assumptions, such a protocol is no more useful than classical schemes for delegating NP-hard problems to the server. Lastly, we comment on the implications of these results for the prospect of verifying a quantum computation through classical interaction with the server.
Blind quantum computing (BQC) ensures that a classical client could delegate complex computing tasks to a remote quantum server safely. In order to detect the dishonest behavior of the participants, we present a verifiable multi-party universal BQC protocol in distributed networks. By using the stabilizer formalism, we propose an honesty check method to test the correctness of the graph states generated by the servers. The honesty of both the clients and the servers can be judged fairly with the help of the arbitrator. Moreover, a load balancer is introduced to control the possible breakdown of servers in the network. No-signaling principle ensures the unconditional security of the protocol. Through the use of universal resource states, our protocol can be applied in more multi-party verifiable universal BQC protocols. The failure management and workload balancing of the protocol also provide a promising prospect for the future BQC network.
Quantum entanglement, a peculiar phenomenon in quantum mechanics, presents a significant challenge to the development of quantum computation. The inherent fragility of entangled states necessitates sophisticated techniques for encoding, transmitting, and analyzing quantum information. This paper proposes a novel method leveraging the unique properties of quantum entanglement to enhance the efficiency and security of quantum computation, focusing on the encoding and analysis of entangled states. The core mechanism centers around utilizing quantum entanglement to achieve enhanced data fidelity and facilitate more robust quantum algorithms. We outline the key steps involved, including the establishment of a secure entanglement distribution protocol, the implementation of a quantum entanglement analysis framework, and the demonstration of its potential impact on quantum algorithm performance. The research explores the practical implications of this approach, emphasizing its capacity to overcome existing limitations and pave the way for significant advancements in quantum information processing.
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.
Blind quantum computation is a new secure quantum computing protocol where a client, who does not have enough quantum technologies at her disposal, can delegate her quantum computation to a server, who has a fully fledged quantum computer, in such a way that the server cannot learn anything about the client's input, output, and program. If the client interacts with only a single server, the client has to have some minimum quantum power, such as the ability of emitting randomly rotated single-qubit states or the ability of measuring states. If the client interacts with two servers who share Bell pairs but cannot communicate with each other, the client can be completely classical. For such a double-server scheme, two servers have to share clean Bell pairs, and therefore the entanglement distillation is necessary in a realistic noisy environment. In this Letter, we show that it is possible to perform entanglement distillation in the double-server scheme without degrading the security of blind quantum computing.