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Paper 1
Quantum Privacy-preserving Two-party Circle Intersection Protocol Based on Phase-encoded Query
Zi-Xian Li, Qi Yang, Bao Feng, Wen-Jie Liu
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2309.17293
- arXiv
- 2309.17293
Privacy-preserving geometric intersection (PGI) is an important issue in Secure multiparty computation (SMC). The existing quantum PGI protocols are mainly based on grid coding, which requires a lot of computational complexity. The phase-encoded query method which has been used in some Quantum SMC protocols is suitable to solve the decision problem, but it needs to apply high dimensional Oracle operators. In this paper, we use the principle of phase-encoded query to solve an important PGI problem, namely privacy-preserving two-party circle intersection. We study the implementation of Oracle operator in detail, and achieve polynomial computational complexity by decompsing it into quantum arithmetic operations. Performance analysis shows that our protocol is correct and efficient, and can protect the privacy of all participants against internal and external attacks.
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From Tensor Networks to Tractable Circuits, and back
Arend-Jan Quist, Marc Farreras Bartra, Alexis de Colnet, John van de Wetering, Alfons Laarman
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2605.00106
- arXiv
- 2605.00106
Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We show that some classes of tensor networks that are appealing in practice correspond to classes of circuits with specific properties that have been studied in knowledge compilation as \emph{tractable circuits}. In particular, we prove that matrix product states (tensor trains) coincide with nondeterministic edge-valued decision diagrams and that tree tensor networks exactly correspond to structured-decomposable circuits. These correspondences enable direct transfer of structural and algorithmic results; for example, canonicity and tractability guarantees known for circuits yield analogous guarantees for the associated tensor networks, and vice versa.
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