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Blind Grover Search for Gate-based Quantum Computers

Alexander Sauer, Alexander von Consbruch, Matthias Zimmermann

Published Mar 13, 2025• 0 citations
OpenAlex

Abstract

hile quantum computers might offer several computational benefits, their application within a quantum network is also of interest in regard to privacy, data protection and computational security. One promising application is blind quantum computing, where a client with limited quantum capacities utilizes the computational power of a quantum computer located at a quantum computing center without revealing any information about the computation or data involved. Several schemes for blind quantum computation have emerged, with the most advanced relying on measurement-based quantum computing [1]. However, many current quantum computer designs are based on gate-based state manipulation. While blind quantum computing is also possible in this scenario, it requires a permanent exchange of quantum information between client and server [2]. To reduce the communication overhead for the involved parties, we study a relaxed scenario of blind quantum computing, where the server gets some information about the algorithm. In particular, we propose a protocol to hide an n-qubit Grover search algorithm by utilizing additional qubits on a quantum server which are initialized by the clients. [1] Fitzsimons, J. F. (2017), npj Quantum Information, 3(1), 23. [2] A. Childs, A. (2005), Quantum Inform. Comput., 5, 456-466.

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hile quantum computers might offer several computational benefits, their application within a quantum network is also of interest in regard to privacy, data protection and computational security. One promising application is blind quantum computing, where a client with limited quantum capacities utilizes the computational power of a quantum computer located at a quantum computing center without revealing any information about the computation or data involved. Several schemes for blind quantum computation have emerged, with the most advanced relying on measurement-based quantum computing [1]. However, many current quantum computer designs are based on gate-based state manipulation. While blind quantum computing is also possible in this scenario, it requires a permanent exchange of quantum information between client and server [2]. To reduce the communication overhead for the involved parties, we study a relaxed scenario of blind quantum computing, where the server gets some information about the algorithm. In particular, we propose a protocol to hide an n-qubit Grover search algorithm by utilizing additional qubits on a quantum server which are initialized by the clients. [1] Fitzsimons, J. F. (2017), npj Quantum Information, 3(1), 23. [2] A. Childs, A. (2005), Quantum Inform. Comput., 5, 456-466.
Known protocols for secure delegation of quantum computations from a client to a server in an information theoretic setting require quantum communication. In this work, we investigate methods to reduce communication overhead. First, we establish an impossibility result by proving that server-side local processes cannot decrease quantum communication requirements of secure delegation protocols. We develop no-go results that prohibit such processes within an information theoretic framework. Second, we present a possibility result by introducing Selectively Blind Quantum Computing (SBQC), a novel functionality that allows the client to hide one among a known set of possible computations. We characterize how differences between computations in the protected set influence the number of qubits sent during our SBQC implementation, yielding a communication-optimal protocol. This approach reduces qubit communication drastically and demonstrates the trade-off between information leaked to the server and communication cost.
Recent years have seen much excitement for application of quantum computing, triggered by substantial — and ongoing — advances in experimental realizations of quantum computing. It is widely believed that client-server is the setting for quantum computers that will prevail in the future, where privacy becomes crucial in the application. Moreover, a recent experiment by Barz et al. [1] successfully demonstrated a blind quantum computation scheme: a 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 valuable details of the computation. In this thesis, we discuss the Blind Oracular Quantum Computation (BOQC) scheme, a blind quantum computing scheme in which a third party (the oracle)with limited quantum power, assists the execution of a client’s oracular quantum computations by implementing oracle evaluations. In BOQC, a client with limited quantum power and without the capacity to construct the oracle, can delegate her oracular quantum computations to a powerful yet untrustworthy server, with the help of the oracle. We show that BOQC is provably blind within a composable definition such that the server cannot learn about the clients’ computation. We provide a realization of BOQC in a physical setting, particularly in a diamond nitrogen-vacancy (NV) center platform. In BOQC, the server has a One-Way Quantum Computer (1WQC) that is resource-demanding. To lower the resource-requirements, we develop the BOQCo protocol, a BOQC that employs lazy 1WQC to minimize the number of qubits needed. We also provide systematic numerical optimization to find resource states that are BOQC-compatible by admitting BOQC security criteria. Finally, we give explicit oracular quantum algorithms that are BOQC-compatible to be executed on the NV-center platform. The algorithms include 2-qubit Grover’s algorithm using three qubits, 3-qubit exact Grover’s algorithm using four qubits, 2-qubit Simon’s algorithm with a useless oracle using four qubits, and Deutsch’s algorithm using three physical qubits. We hope that these BOQC algorithms intrigue some experimentalists to try to implement them.[1] S. Barz et al. “Demonstration of Blind Quantum Computing”. In: Science 335.6066 (2012), pp. 303–308.
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.
It is called blind quantum computation(BQC) that a client who has limited quantum technologies can delegate her quantum computing to a server who has fully-advanced quantum computers. But the privacy of the client's quantum inputs, algorithms and outputs is still a challenge. To realize a secure BQC, we mainly study how to hide quantum fourier transform (QFT) performed on Bell states. In this paper, three cases are considered as follows. For the first case, we design primary BQC protocols of QFT performed on qubits 12 of belonging to {∣ϕ±⟩12,\{|ϕ^\pm\rangle_{12},{∣ϕ±⟩12​, ∣ψ±⟩12}|ψ^\pm\rangle_{12}\}∣ψ±⟩12​} with relevant circuits. To strengthen security, we construct enhanced BQC protocols of QFT performed on qubits 13 of any two Bell states ∣ξ⟩12⊗∣θ⟩34|ξ\rangle_{12}\otimes|θ\rangle_{34}∣ξ⟩12​⊗∣θ⟩34​ with relevant quantum circuits. Featured the property of stronger security, we give generalized BQC protocols of QFT performed on qubits 13 and 24 of any two Bell states with relevant quantum circuits respectively. At last, we analyze and prove the blindness and correctness.
Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.
Blind quantum computation (BQC) is a recent proposition in which a computation is performed on a server by a client in a manner that the server is kept blind about the input, the algorithm and the output of the computation. This model possesses a natural security, which makes it suitable for applications where privacy matters. In this paper we propose a framework for BQC which can be implemented by circuit models as well as measurement-based models of quantum computation. It is based on gate teleportation, a process in which by storing one-qubit gates in entangled pairs one can apply it later via teleportation. We elaborate on examples of such universal BQC (UBQC) protocols. Specially, we elaborate on UBQC for correlation-space measurement-based quantum computation.