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| Autores principales: | , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | https://arxiv.org/abs/2112.09349 |
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| _version_ | 1866918187430313984 |
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| author | Basili, Robert A. M. Qian, Wenyang Sarker, Shiplu Tang, Shuo Castellino, Austin Eshaghian-Wilner, Mary Khokhar, Ashfaq Luecke, Glenn Vary, James P. |
| author_facet | Basili, Robert A. M. Qian, Wenyang Sarker, Shiplu Tang, Shuo Castellino, Austin Eshaghian-Wilner, Mary Khokhar, Ashfaq Luecke, Glenn Vary, James P. |
| contents | The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor's algorithm, weighted sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM's superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands' superposed integer states. We analyze performance, and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. We analyze the performance trends in our results and speculate on possible future developments within this computational paradigm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09349 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Performance Evaluations of Signed and Unsigned Noisy Approximate Quantum Fourier Arithmetic Basili, Robert A. M. Qian, Wenyang Sarker, Shiplu Tang, Shuo Castellino, Austin Eshaghian-Wilner, Mary Khokhar, Ashfaq Luecke, Glenn Vary, James P. Quantum Physics The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor's algorithm, weighted sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM's superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands' superposed integer states. We analyze performance, and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. We analyze the performance trends in our results and speculate on possible future developments within this computational paradigm. |
| title | Performance Evaluations of Signed and Unsigned Noisy Approximate Quantum Fourier Arithmetic |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2112.09349 |