A general framework for the composition of quantum homomorphic
encryption \& quantum error correction
- URL: http://arxiv.org/abs/2204.10471v1
- Date: Fri, 22 Apr 2022 02:47:07 GMT
- Title: A general framework for the composition of quantum homomorphic
encryption \& quantum error correction
- Authors: Yingkai Ouyang and Peter P. Rohde
- Abstract summary: Two essential primitives for universal, cloud-based quantum computation are quantum homomorphic encryption with information-theoretic security and quantum error correction.
We apply our framework to both discrete- and continuous-variable models for quantum computation.
- Score: 6.85316573653194
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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