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Paper 1
The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic
G. Papakonstantinou
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2512.12073
- arXiv
- 2512.12073
Efficient arithmetic operations are a prerequisite for practical quantum computing. Optimization efforts focus on two primary metrics: Quantum Cost (QC), determined by the number of non-linear gates, and Logical Depth, which defines the execution speed. Existing literature identifies the HNG gate as the standard for Input-Preserving Reversible Full Adders. HNG gate typically requires a QC of 12 and a logical depth of 5, in the area of classical reversible circuits. This paper proposes the PPKN Gate, a novel design that achieves the same inputpreserving functionality using only one Toffoli gate and five CNOT gates. With a Quantum Cost of 10 and a reduced logical depth of 4, the PPKN gate outperforms the standard HNG gate in both complexity and speed. Furthermore, we present a modular architecture for constructing an n-bit Ripple Carry Adder by cascading PPKN modules.
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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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