Quantum adders: on the structural link between the ripple-carry and carry-lookahead techniques
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914070391685120 |
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| author | Remaud, Maxime |
| author_facet | Remaud, Maxime |
| contents | This paper is motivated by two key observations. First, Toffoli ladders can be implemented in three distinct ways: with linear or polylogarithmic depth using no ancilla, or with logarithmic depth using ancilla qubits. Second, two fundamental structural approaches to designing addition algorithms can be identified in several well-known quantum adders. At their core is the Toffoli ladder, and both provide a clear and simple connection between ripple-carry and carry-lookahead adder designs. Combining these two structures with the three Toffoli ladder implementations yields six quantum adders: four are well-known and two novel. Notably, one of the novel designs is a carry-lookahead adder that outperforms previous approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum adders: on the structural link between the ripple-carry and carry-lookahead techniques Remaud, Maxime Quantum Physics This paper is motivated by two key observations. First, Toffoli ladders can be implemented in three distinct ways: with linear or polylogarithmic depth using no ancilla, or with logarithmic depth using ancilla qubits. Second, two fundamental structural approaches to designing addition algorithms can be identified in several well-known quantum adders. At their core is the Toffoli ladder, and both provide a clear and simple connection between ripple-carry and carry-lookahead adder designs. Combining these two structures with the three Toffoli ladder implementations yields six quantum adders: four are well-known and two novel. Notably, one of the novel designs is a carry-lookahead adder that outperforms previous approaches. |
| title | Quantum adders: on the structural link between the ripple-carry and carry-lookahead techniques |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.00840 |