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arXiv:2503.09099

Simulation of Two-Qubit Grover Algorithm in MBQC with Universal Blind Quantum Computation

Youngkyung Lee, Doyoung Chung

Published Mar 12, 2025• 0 citations
arXivHTMLPDF

Abstract

Simulating the Universal Blind Quantum Computation (UBQC) protocol on gate-based platforms requires updating each measurement basis from earlier outcomes within the same execution. Existing Measurement-Based Quantum Computation (MBQC) simulation tools typically handle this feed-forward outside a single executable quantum program, so they do not natively expose the fixed-graph measurement-by-measurement update order studied here. We address this gap by implementing the flow-based Pauli corrections and a simulation-level UBQC angle-update rule as in-circuit dynamic-circuit primitives in Qiskit. Applied to two-qubit Grover's algorithm on a custom $2\times 9$ flow of 18 qubits, the resulting program achieves deterministic success under both plain MBQC and the UBQC layer. Under the depolarizing-noise setting considered here, the angle-blinding layer remains close to plain MBQC, with only a modest additional gap relative to the dominant MBQC-over-circuit overhead. To show that the construction is not tied only to this Grover-specific pattern, we also verify a $G_{2,5}$ brickwork-state fragment with representative universal-gate primitives under the same client/server blinding view. Structural blindness for a full algorithmic brickwork resource remains future work, but within this scope the construction provides a concrete dynamic-circuit route toward fixed-graph, privacy-preserving delegated-quantum-computing simulation at the protocol-update level.

DOI
10.48550/arxiv.2503.09099

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Simulating the Universal Blind Quantum Computation (UBQC) protocol on gate-based platforms requires updating each measurement basis from earlier outcomes within the same execution. Existing Measurement-Based Quantum Computation (MBQC) simulation tools typically handle this feed-forward outside a single executable quantum program, so they do not natively expose the fixed-graph measurement-by-measurement update order studied here. We address this gap by implementing the flow-based Pauli corrections and a simulation-level UBQC angle-update rule as in-circuit dynamic-circuit primitives in Qiskit. Applied to two-qubit Grover's algorithm on a custom 2×92\times 92×9 flow of 18 qubits, the resulting program achieves deterministic success under both plain MBQC and the UBQC layer. Under the depolarizing-noise setting considered here, the angle-blinding layer remains close to plain MBQC, with only a modest additional gap relative to the dominant MBQC-over-circuit overhead. To show that the construction is not tied only to this Grover-specific pattern, we also verify a G2,5G_{2,5}G2,5​ brickwork-state fragment with representative universal-gate primitives under the same client/server blinding view. Structural blindness for a full algorithmic brickwork resource remains future work, but within this scope the construction provides a concrete dynamic-circuit route toward fixed-graph, privacy-preserving delegated-quantum-computing simulation at the protocol-update level.
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.
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.
Universal blind quantum computation allows a client who has limited quantum abilities to delegate his or her private computation to an untrusted quantum server. The first universal blind quantum computation protocol was proposed by Broadbent, Fitzsimons, and Kashefi. In their work the computation resource is the so-called brickwork state, which can be constructed by a number of specific single qubits. The number of single qubits is in theory linearly related to the size of the quantum circuit. However, due to the fixed structure of the brickwork states, the actual number of qubits is usually far more than the linear size. In this work we mainly construct three improved brickwork states whose structures are no longer fixed, thus they can efficiently reduce the client's qubit consumption. Using those improved brickwork states we propose a class of efficient universal blind quantum computation protocols. In our basic protocol, to implement a single-qubit basic gate the client needs to prepare only two ancillary qubits, while in the original protocol it will consume four ancillary qubits. Making use of our improved brickwork states the qubit consumption of implementing a nonadjacent two-qubit gate such as a control-XXX gate can be sharply reduced.
Blind quantumcomputation protocols allowa 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 quantumdevices: 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 server. Specifically, we show how a classical client can exploit the ambiguity in the flowof information inmeasurement-based quantumcomputing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there existmultiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.
The universal blind quantum computation (UBQC) protocol [A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual IEEE Symposiumon Foundations of Computer Science (IEEE Computer Society, Los Alamitos, CA, USA, 2009), pp. 517-526.] allows a client to perform quantum computation on a remote server. In an ideal setting, perfect privacy is guaranteed if the client is capable of producing specific, randomly chosen single qubit states. While from a theoretical point of view, this may constitute the lowest possible quantum requirement, from a pragmatic point of view, generation of such states to be sent along long distances can never be achieved perfectly. We introduce the concept of ϵ blindness for UBQC, in analogy to the concept of ϵ security developed for other cryptographic protocols, allowing us to characterize the robustness and security properties of the protocol under possible imperfections. We also present a remote blind single qubit preparation protocol with weak coherent pulses for the client to prepare, in a delegated fashion, quantum states arbitrarily close to perfect random single qubit states. This allows us to efficiently achieve ϵ-blind UBQC for any ϵ>0, even if the channel between the client and the server is arbitrarily lossy.
Blind quantum computation (BQC) allows that a client who has limited quantum abilities can delegate quantum computation to a server who has advanced quantum technologies but learns nothing about the client's private information. However, it still remains a challenge to directly encrypt quantum algorithms in circuits model. To solve the problem, we propose GTUBQC, the first gate teleportation-based universal BQC protocol. In this paper, we consider a scenario where a trusted center is responsible for preparing initial states, a client with the ability to perform X, Z does not require any quantum memory, and two servers conducting UBQC (universal BQC) and Bell measurements. GTUBQC can hide the universal quantum gates by encrypting the rotation angles, because arbitrary unitary operation can be decomposed into a combination of arbitrary rotation operators. We prove the blindness and correctness of GTUBQC, and apply our approach to other types of computational tasks, such as quantum Fourier transform.