The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917148196077568 |
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| author | Papakonstantinou, G. |
| author_facet | Papakonstantinou, G. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_12073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic Papakonstantinou, G. Quantum Physics Emerging Technologies 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. |
| title | The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2512.12073 |