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arXiv:2106.15770 · Physical Review A

Variational secure cloud quantum computing

Yuta Shingu, Yuki Takeuchi, Suguru Endo, Shiro Kawabata, Shohei Watabe, Tetsuro Nikuni, Hideaki Hakoshima, Yuichiro Matsuzaki

Published Feb 3, 2022• 10 citations
arXivHTMLPDF

Abstract

Variational quantum algorithms (VQAs) have been considered to be useful applications of noisy intermediate-scale quantum (NISQ) devices. Typically, in VQAs, a parametrized ansatz circuit is used to generate a trial wave function, and the parameters are optimized to minimize a cost function. On the other hand, blind quantum computing (BQC) has been studied in order to provide a quantum algorithm with security by using cloud networks. A client with a limited ability to perform quantum operations hopes to have access to a quantum computer of a server, and BQC allows the client to use the server's computer without leakage of the client's information (such as input, running quantum algorithms, and output) to the server. However, BQC is designed for fault-tolerant quantum computing, and this requires many ancillary qubits, which may not be suitable for NISQ devices. Here, we propose an efficient way to implement the NISQ computing with guaranteed security for the client. In our architecture, only $N+1$ qubits are required, under an assumption that the form of ans\"atze is known to the server, where $N$ denotes the necessary number of the qubits in the original NISQ algorithms. The client only performs single-qubit measurements on an ancillary qubit sent from the server, and the measurement angles can specify the parameters for the ans\"atze of the NISQ algorithms. The no-signaling principle guarantees that neither parameters chosen by the client nor the outputs of the algorithm are leaked to the server. This work paves the way for new applications of NISQ devices.

DOI
10.1103/physreva.105.022603

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Variational quantum algorithms (VQAs) have been considered to be useful applications of noisy intermediate-scale quantum (NISQ) devices. Typically, in VQAs, a parametrized ansatz circuit is used to generate a trial wave function, and the parameters are optimized to minimize a cost function. On the other hand, blind quantum computing (BQC) has been studied in order to provide a quantum algorithm with security by using cloud networks. A client with a limited ability to perform quantum operations hopes to have access to a quantum computer of a server, and BQC allows the client to use the server's computer without leakage of the client's information (such as input, running quantum algorithms, and output) to the server. However, BQC is designed for fault-tolerant quantum computing, and this requires many ancillary qubits, which may not be suitable for NISQ devices. Here, we propose an efficient way to implement the NISQ computing with guaranteed security for the client. In our architecture, only N+1N+1N+1 qubits are required, under an assumption that the form of ans"atze is known to the server, where NNN denotes the necessary number of the qubits in the original NISQ algorithms. The client only performs single-qubit measurements on an ancillary qubit sent from the server, and the measurement angles can specify the parameters for the ans"atze of the NISQ algorithms. The no-signaling principle guarantees that neither parameters chosen by the client nor the outputs of the algorithm are leaked to the server. This work paves the way for new applications of NISQ devices.
Variational quantum algorithms (VQAs) are considered as one of the most promising candidates for achieving quantum advantages on quantum devices in the noisy intermediate-scale quantum (NISQ) era. They have been developed for numerous applications such as image processing and solving linear systems of equations. The application of VQAs can be greatly enlarged if users with limited quantum capabilities can run them on remote powerful quantum computers. But the private data of clients may be leaked to quantum servers in such a quantum cloud model. To solve the problem, a novel quantum homomorphic encryption (QHE) scheme which is client-friendly and suitable for VQAs is constructed for quantum servers to calculate encrypted data. Then delegated VQAs are proposed based on the given QHE scheme, where the server can train the ansatz circuit using the client's data even without knowing the real input and the output of the client. Furthermore, a delegated variational quantum classifier to identify handwritten digit images is given as a specific example of delegated VQAs and simulated on the cloud platform of Original Quantum to show its feasibility.
Variational quantum algorithms (VQAs) can train parameterized quantum circuits via classical optimizers to find approximate solutions to some important problems. They can overcome the limitations of existing quantum technologies only allowing for a few qubits and small circuit depth and are considered as one of the most promising methods for achieving quantum advantages in the noisy intermediate-scale quantum (NISQ) era. In this paper, we propose secure delegated VQAs by utilizing quantum homomorphic encryption (QHE) for users with limited quantum power to delegate the task of running VQAs to remote quantum servers while still keeping the training data private. Firstly, a client-friendly QHE scheme that allows quantum servers to perform calculation on encrypted data is proposed to be suitable for VQAs. Then, delegated VQAs based on the given QHE scheme are presented, where servers can train the ansatz circuit using the encrypted data. Finally, a delegated variational quantum classifier to identify handwritten digit images is given as a specific example of delegated VQAs and simulated on the cloud platform of Original Quantum to show the feasibility. Secure delegated VQAs will provide significant technical support for future quantum cloud services.
In the noisy intermediate-scale quantum (NISQ) era, quantum computing resources are increasingly provided through cloud platforms, enabling users to perform quantum computations without owning expensive hardware. However, delegating computations to remote servers raises a key challenge: ensuring the privacy of the client’s input, algorithm, and output. To address this issue, we propose a circuit-model blind quantum computation (CMBQC) protocol that conceals the target quantum computation while decoupling the encryption and decryption keys. This key-decoupled structure avoids gate-by-gate propagation of decryption information on the client side. We establish blindness of the target operation within its Pauli equivalence class and prove the verifiability of the protocol, where verification is achieved by estimating expectation values of randomly chosen Pauli observables, thereby substantially reducing the verification overhead. We further demonstrate a single-qubit implementation of the CMBQC protocol on an International Business Machines Corporation (IBM) superconducting quantum system. The simple structure and low verification cost of the CMBQC protocol make it a promising framework for secure delegated quantum computation, with potential applications in quantum cloud computing.
Current cloud-based quantum processors offer access to advanced hardware hosted on a remote server, but do not guarantee data or algorithm privacy. Blind quantum computation provides information-theoretic privacy by enabling a client to execute an algorithm without disclosing information about either the task or the final result. Here, we execute a measurement-based blind quantum computation protocol on a superconducting processor comprising two flip-chip-bonded modules, one acting as a server and the other as a client. The server generates a two-dimensional cluster state and forwards it to the client. Using this resource, the client implements a universal gate set with only adaptive single-qubit rotations and measurements. To illustrate this approach, we execute a three-qubit instance of the Deutsch-Jozsa algorithm. We analyze the server's quantum state after each rotation of a measurement-based single-qubit gate to verify that negligible information about the computation is revealed to the server, consistent with the one-way flow of information that guarantees blindness. This proof-of-principle demonstration establishes key elements of blind quantum computation in superconducting-circuit architectures, indicating that intermediate-scale implementations of blind protocols may become feasible with realistic near-term improvements in gate fidelities.
Variational quantum algorithms (VQAs) have emerged as promising candidates for solving complex optimization and machine learning tasks on near-term quantum hardware. However, executing quantum operations remains challenging for small-scale users because of several hardware constraints, making it desirable to delegate parts of the computation to more powerful quantum devices. In this work, we introduce a framework for delegated variational quantum algorithms, where a client with limited quantum capabilities delegates the execution of a VQA to a more powerful quantum server. In particular, we introduce a protocol that enables a client to delegate a variational quantum algorithm to a server while ensuring that the input, the output, and also the computation itself remain secret. Additionally, if the protocol does not abort, the client can be certain that the computation outcome is indeed correct. This work builds on the general verification protocol introduced by Fitzsimons and Kashefi [], tailoring it to VQAs. Our approach first proposes a verifiable protocol for delegating the quantum computation at each optimization step of a VQA and then combines the iterative steps into an error-resilient optimization process that offers end-to-end verifiable algorithm execution. We also simulate the performance of our protocol tackling the transverse field Ising model. Our results demonstrate that secure delegation of variational quantum algorithms is a realistic solution for near-term quantum networks, paving the way for practical quantum cloud computing applications.
Blind quantum computing (BQC) allows a client to delegate quantum computations to a remote server without revealing the input, computation, or output. In addition to being blind, the client can sometimes also verify that the server has performed their instructions correctly, a property known as verifiability. A key part of realizing such verifiable BQC (VBQC) is choosing the design of the client device: many architectures have been proposed, each with different hardware requirements, security properties, and performance characteristics, making it difficult to identify which is most suitable for a given implementation. In this work, we present a comparative analysis of client architectures for VBQC with a matter-qubit server. We restrict our analysis to single-server, single-client protocols with information-theoretic security based on measurement-based quantum computation. We identify three main categories of client: emission-based, measurement-based, and rotation-based, each with multiple variants depending on how the client interacts with the server. We evaluate each across different dimensions: we compare guarantees of existing corresponding security proofs, we derive equations for the rate at which each client can execute a protocol, we provide an overview of each architecture's error behaviour, and discuss hardware cost and design considerations. Client architectures implementing measurement-based remote state preparation and reflection-based teleportation emerge as strong default candidates, but as the right choice remains context-dependent, we provide a framework for navigating considerations to guide the selection of the most suitable architecture for a given setting.