🤖 AI Summary
This work addresses the fundamental challenge of integrating quantum homomorphic encryption (QHE) with fault-tolerant quantum error correction (QEC) in cloud-based quantum computing. Methodologically, it introduces the first information-theoretically secure, general-purpose integration framework, featuring a novel group-theoretic constraint that enables modular composition of QHE schemes—supporting Pauli, permutation, and GKP displacement keys—with homomorphic QEC codes, including the GKP code, without requiring encrypted permutation keys for end-to-end encoding/decoding. The contributions are threefold: (i) unified treatment of both discrete- and continuous-variable quantum models; (ii) rigorous proof that the composed system simultaneously satisfies semantic security, homomorphism, information-theoretic security, and fault-tolerant robustness; and (iii) establishment of a theoretical foundation and architectural blueprint for scalable, secure cloud quantum computation.
📝 Abstract
Two essential primitives for universal, cloud-based quantum computation with security based on the laws of quantum mechanics, are quantum homomorphic encryption with information-theoretic security and quantum error correction. The former enables information-theoretic security of outsourced quantum computation, while the latter allows reliable and scalable quantum computations in the presence of errors. Previously these ingredients have been considered in isolation from one another. By establishing group-theoretic requirements that these two ingredients must satisfy, we provide a general framework for composing them. Namely, a quantum homomorphic encryption scheme enhanced with quantum error correction can directly inherit its properties from its constituent quantum homomorphic encryption and quantum error correction schemes. We apply our framework to both discrete- and continuous-variable models for quantum computation, such as Pauli-key and permutation-key encryptions in the qubit model, and displacement-key encryptions in a continuous-variable model based on Gottesman-Kitaev-Preskill codes.
