Quantum computing on encrypted data with arbitrary rotation gates

2025-08-26

AI Summary

Existing semi-blind quantum computation (SBQC) protocols support only fixed, non-parametric gates (e.g., H, S, T, CX), limiting expressivity for encrypted quantum computations requiring arbitrary parameterized rotations such as $R_z( heta)$. Method: We propose the first SBQC protocol supporting arbitrary parametrized single-qubit rotations. Our approach introduces a recursive decryption mechanism enabling exact and high-precision approximate implementation of $R_z( heta)$, integrated with lightweight interactive verification, parameterized gate compilation, and optimized circuit architecture. Contribution/Results: This is the first SBQC scheme achieving universal parametrized gate evaluation. It reduces both computational and communication complexity to $O(log^2(pi/varepsilon))$, improving upon the prior best $O(log^{3.97}(1/varepsilon))$. Circuit depth is significantly compressed, enhancing practicality and scalability of secure quantum computation in the NISQ era.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

An efficient technique of computing on encrypted data allows a client with limited capability to perform complex operations on a remote fault-tolerant 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, they are dependent on a fixed non-parametric resource set that comprises some universal combination of $H,S,T,CX, CZ$ or $CCX$ gates. In this study, we show that recursive decryption of the parametric gate, $R_z(θ)$, is possible exactly when $θ=pmπ/2^m$ for $min mathbb{Z^{+}}$, and approximately with arbitrary precision $ε$ for 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 $O(ln^{3.97}(1/ε))$ rounds. We use these results to propose a universal scheme of half-blind quantum computation for computing on encrypted data using arbitrary rotation gates. This substantial reduction in the depth of blind circuit is an affirmative step towards the practical application of such techniques in secure NISQ-era computing.

Problem

• Enabling arbitrary rotation gates in encrypted quantum computation
• Reducing computational steps for blind quantum algorithms
• Achieving practical secure computing in NISQ-era systems

Innovation

• Exact recursive decryption for specific rotation angles
• Approximate decryption with arbitrary precision for any angle
• Reduced computation steps and communication rounds