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arXiv:2508.18811 · Physica Scripta

Quantum computing on encrypted data with arbitrary rotation gates

Mohit Joshi, Manoj Kumar Mishra, Karthikeyan Subbiah

Published May 15, 2026• 0 citations
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Abstract

Abstract An efficient technique of computing on encrypted data allows a client with limited capability to perform complex operations on a powerful remote server without leaking anything about the input or output. Quantum computing provides information-theoretic security to solve such a problem, and many such techniques have been proposed under the premises of half-blind quantum computation. However, these approaches are based on some universal combination of non-parametric gates ( H , S , T , C X , C Z , and C C X ). Hybrid quantum–classical algorithms require parametric gates, which, when decomposed into non-parametric gates, inadvertently increase the depth of the circuit and hence the communication rounds. We propose an approach for recursive decryption of any parametric gate, R z ( θ ) , without prior decomposition; exactly when θ = ± π / 2 m for m ∈ Z + , and approximately with arbitrary precision ϵ for any given θ . We also show that a blind algorithm based on such a technique needs at most O ( log 2 2 ⁡ ( π / ϵ ) ) computation steps and communication rounds, while the techniques based on a non-parametric resource set require O ( ln 3.97 ⁡ ( 1 / ϵ ) ) . We use this approach to propose a half-blind quantum computation protocol to enable efficient computation on encrypted data in the NISQ era.

DOI
10.1088/1402-4896/ae6e9c

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Abstract An efficient technique of computing on encrypted data allows a client with limited capability to perform complex operations on a powerful remote server without leaking anything about the input or output. Quantum computing provides information-theoretic security to solve such a problem, and many such techniques have been proposed under the premises of half-blind quantum computation. However, these approaches are based on some universal combination of non-parametric gates ( H , S , T , C X , C Z , and C C X ). Hybrid quantum–classical algorithms require parametric gates, which, when decomposed into non-parametric gates, inadvertently increase the depth of the circuit and hence the communication rounds. We propose an approach for recursive decryption of any parametric gate, R z ( θ ) , without prior decomposition; exactly when θ = ± π / 2 m for m ∈ Z + , and approximately with arbitrary precision ϵ for any given θ . We also show that a blind algorithm based on such a technique needs at most O ( log 2 2 ⁡ ( π / ϵ ) ) computation steps and communication rounds, while the techniques based on a non-parametric resource set require O ( ln 3.97 ⁡ ( 1 / ϵ ) ) . We use this approach to propose a half-blind quantum computation protocol to enable efficient computation on encrypted data in the NISQ era.
Blind Quantum Computation lets a limited-capability client delegate its complex computation to a remote server without revealing its data or computation. Several such protocols have been proposed under varied quantum computing models. However, these protocols either rely on highly entangled resource states (in measurement-based models) or are based on non-parametric resource sets (in circuit-based models). These restrictions hinder the practical applicability of such an algorithm in the NISQ era, especially concerning the hybrid quantum-classical infrastructure, which depends on parametric gates. We present a protocol for universal blind quantum computation based on recursive decryption of parametric rotation gates, which does not require a highly entangled state at the server side and substantially reduces the communication rounds required for practical prototyping of secure variational algorithms.
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.
Blind quantum computation (BQC) allows a client who has a few quantum abilities to interact and delegate her quantum computation to a server that has strong quantum computabilities, while the server learns nothing about client’s quantum inputs, algorithms, and outputs. In this article, a new BQC protocol with hybrid model is proposed, using the combination of rotation operators to construct arbitrary quantum gate. Our BQC protocol is divided into two phases. In the first phase, a new kind of function operation is designed and defined, that is, the client sends the classical message [Formula: see text] to the server and then the sever performs a corresponding function operation [Formula: see text], which has been defined. In the second phase, a rotation operator or identity operator is implemented by quantum gate teleportation where the server can’t know which quantum gate has been teleported. Combining these two phases, the server has no idea about client’s quantum algorithms. When the server performs the corresponding operation honestly, the client only needs to perform [Formula: see text] and [Formula: see text] operators.
Abstract Quantum computing on encrypted data allows a client who has limited quantum capacity to delegate his or her private computation to an untrusted quantum server, while the input and output are encrypted by the quantum one-time pad and only the client can correctly decrypt them. Generally, the client is required to have ability to prepare some single qubits and perform some basic gates. In this work, we consider a further restricted situation where the client can only prepare one single qubit and perform one basic gate. Specifically, we show that as long as the client can prepare a fixed qubit and perform a fixed phase gate P , then he or she can still achieve the secure delegated quantum computation. Besides, our protocol can provide a more rigorous security for any quantum computation. For example, even if some encryption keys about the computation are leaked, it can still guarantee the privacy of the input and output. Finally, our protocol experimentally has a great significance in reducing the device complexity of the client's side.
Abstract Quantum computers promise not only to outperform classical machines for certain important tasks, but also to preserve privacy of computation. For example, the blind quantum computing protocol enables secure delegated quantum computation, where a client can protect the privacy of their data and algorithms from a quantum server assigned to run the computation. However, this security comes with the practical limitation that the client and server must communicate after each step of computation. A practical alternative is homomorphic encryption, which does not require any interactions, while providing quantum-enhanced data security for a variety of computations. In this scenario, the server specifies the computation to be performed, and the client provides only the input data, thus enabling secure noninteractive computation. Here, we demonstrate homomorphic-encrypted quantum computing with unitary transformations of individual qubits, as well as multi-qubit quantum walk computations using single-photon states and non-birefringent integrated optics. The client encrypts their input in the photons’ polarization state, while the server performs the computation using the path degree of freedom. Our demonstration using integrated quantum photonics underlines the applicability of homomorphic-encrypted quantum computations, and shows the potential for delegated quantum computing using photons.
Abstract Blind quantum computation enables a client with limited quantum capabilities to delegate a powerful quantum computer for performing confidential quantum computation. This paper identifies a security loophole in the initial universal half-blind quantum computation protocol and resolves it using operation teleportation. Simultaneously, to minimize quantum resource consumption for both the client and the server, the proposed protocol relies on the universal gate set H, T, and CX, and only necessitates the client’s ability to prepare qubits in the eigenstates of Pauli gates X and Y or measure qubits based on these gates. Finally, a sample example is provided to illustrate the proposed protocol effectively.