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Paper 1
Quantum CNOT Circuits Synthesis for NISQ Architectures Using the Syndrome Decoding Problem
de Brugière T, Baboulin M, Valiron B, Martiel S, Allouche C.
- Year
- 2020
- Journal
- Reversible Computation12th International Conference, RC 2020, Oslo, Norway, July 9-10, 2020, Proceedings
- DOI
- EuropePMC:PMC:PMC7345310
- arXiv
- -
No abstract.
Open paperPaper 2
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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