Quantum Arithmetic Algorithms: Implementation, Resource Estimation, and Comparison
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866911297497464832 |
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| author | Fedoriaka, Dmytro Goldsmith, Brian Chen, Yingrong |
| author_facet | Fedoriaka, Dmytro Goldsmith, Brian Chen, Yingrong |
| contents | As quantum computing technology advances, the need for optimized arithmetic circuits continues to grow. This paper presents the implementation and resource estimation of a library of quantum arithmetic algorithms, including addition, multiplication, division, and modular exponentiation. Using the Azure Quantum Resource Estimator, we evaluate runtime, qubit usage, and space-time trade-offs and identify the best-performing algorithm for each arithmetic operation. We explore the design space for division, optimize windowed modular exponentiation, and identify the tipping point between multipliers, demonstrating effective applications of resource estimation in quantum research. Additionally, we highlight the impact of parallelization, reset operations, and uncomputation techniques on implementation and resource estimation. Our findings provide both a practical library and a valuable knowledge base for selecting and optimizing quantum arithmetic algorithms in real-world applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Arithmetic Algorithms: Implementation, Resource Estimation, and Comparison Fedoriaka, Dmytro Goldsmith, Brian Chen, Yingrong Quantum Physics As quantum computing technology advances, the need for optimized arithmetic circuits continues to grow. This paper presents the implementation and resource estimation of a library of quantum arithmetic algorithms, including addition, multiplication, division, and modular exponentiation. Using the Azure Quantum Resource Estimator, we evaluate runtime, qubit usage, and space-time trade-offs and identify the best-performing algorithm for each arithmetic operation. We explore the design space for division, optimize windowed modular exponentiation, and identify the tipping point between multipliers, demonstrating effective applications of resource estimation in quantum research. Additionally, we highlight the impact of parallelization, reset operations, and uncomputation techniques on implementation and resource estimation. Our findings provide both a practical library and a valuable knowledge base for selecting and optimizing quantum arithmetic algorithms in real-world applications. |
| title | Quantum Arithmetic Algorithms: Implementation, Resource Estimation, and Comparison |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.07015 |