Optimal Toffoli-Depth Quantum Adder
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914783830212608 |
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| author | Wang, Siyi Deb, Suman Mondal, Ankit Chattopadhyay, Anupam |
| author_facet | Wang, Siyi Deb, Suman Mondal, Ankit Chattopadhyay, Anupam |
| contents | Efficient quantum arithmetic circuits are commonly found in numerous quantum algorithms of practical significance. Till date, the logarithmic-depth quantum adders includes a constant coefficient k >= 2 while achieving the Toffoli-Depth of klog n + O(1). In this work, 160 alternative compositions of the carry-propagation structure are comprehensively explored to determine the optimal depth structure for a quantum adder. By extensively studying these structures, it is shown that an exact Toffoli-Depth of log n + O(1) is achievable. This presents a reduction of Toffoli-Depth by almost 50% compared to the best known quantum adder circuits presented till date. We demonstrate a further possible design by incorporating a different expansion of propagate and generate forms, as well as an extension of the modular framework. Our paper elaborates on these designs, supported by detailed theoretical analyses and simulation-based studies, firmly substantiating our claims of optimality. The results also mirror similar improvements, recently reported in classical adder circuit complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02523 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Toffoli-Depth Quantum Adder Wang, Siyi Deb, Suman Mondal, Ankit Chattopadhyay, Anupam Quantum Physics Emerging Technologies Efficient quantum arithmetic circuits are commonly found in numerous quantum algorithms of practical significance. Till date, the logarithmic-depth quantum adders includes a constant coefficient k >= 2 while achieving the Toffoli-Depth of klog n + O(1). In this work, 160 alternative compositions of the carry-propagation structure are comprehensively explored to determine the optimal depth structure for a quantum adder. By extensively studying these structures, it is shown that an exact Toffoli-Depth of log n + O(1) is achievable. This presents a reduction of Toffoli-Depth by almost 50% compared to the best known quantum adder circuits presented till date. We demonstrate a further possible design by incorporating a different expansion of propagate and generate forms, as well as an extension of the modular framework. Our paper elaborates on these designs, supported by detailed theoretical analyses and simulation-based studies, firmly substantiating our claims of optimality. The results also mirror similar improvements, recently reported in classical adder circuit complexity. |
| title | Optimal Toffoli-Depth Quantum Adder |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2405.02523 |