Computational complexity and applications of quantum algorithm
We have studied on quantum algorithm several years, and introduced a mathematical model of it in order to discuss the computational complexity. Our model of quantum algorithm, called a generalized quantum Turing machine (GQTM) contains not only unitary computation process but also quantum measuremen...
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| Vydané v: | Applied mathematics and computation Ročník 218; číslo 16; s. 8019 - 8028 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
15.04.2012
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| Abstract | We have studied on quantum algorithm several years, and introduced a mathematical model of it in order to discuss the computational complexity. Our model of quantum algorithm, called a generalized quantum Turing machine (GQTM) contains not only unitary computation process but also quantum measurement and dissipative process. Moreover, we discovered that a chaos dynamics has very important role in quantum algorithm, that is useful to solve NP complete problem in polynomial time. In this paper, we introduce the GQTM and some applications. |
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| AbstractList | We have studied on quantum algorithm several years, and introduced a mathematical model of it in order to discuss the computational complexity. Our model of quantum algorithm, called a generalized quantum Turing machine (GQTM) contains not only unitary computation process but also quantum measurement and dissipative process. Moreover, we discovered that a chaos dynamics has very important role in quantum algorithm, that is useful to solve NP complete problem in polynomial time. In this paper, we introduce the GQTM and some applications. |
| Author | Iriyama, S. Ohya, M. |
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| Keywords | Quantum Turing machine Computational complexity Quantum algorithm |
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| References | Iriyama, Ohya (b0075) 2009; II S. Iriyama, M. Ohya, The problem to construct Unitary Quantum Turing Machine computing partial recursive functions, TUS preprint, 2009. S. Iriyama, M. Ohya, Quantum Algorithm for Pebble Game and Its Computational Complexity, TUS preprint, 2010. E. Bernstein, U. Vazirani, Quantum complexity theory, in: Proceedings of the 25th Annual ACM Symposium on Theory of Computing, ACM, New York, 1993, pp.11–22. SIAM Journal on Computing 26, 1411, 1997. Asano, Ohya, Khrennikov (b0105) 2010 Ohya, Masuda (b0015) 2000; 7 Accardi, Ohya (b0040) 2004; 11 Iriyama, Ohya (b0065) 2008; 15 Ohya (b0030) 1998; 37 S. Iriyama, M. Ohya, K. Sato, I.V. Volovich, Photosynthetic Antenna and Entropy Decreasing, in preparation. Ohya, Volovich (b0005) 2003; 5 S. Iriyama, M. Ohya, I. Yamato, Quantum Algorithm of Protain Folding, TUS preprint, 2010. Deutsch (b0020) 1985; 400 Khrennikov (b0100) 2010 Iriyama, Miyadera, Ohya (b0060) 2008; 372 Accardi, Ohya (b0035) 1999; 39 L. Accardi, R. Sabbadini, On the Ohya–Masuda quantum SAT Algorithm, Preprint Volterra, N. 432, 2000. Ohya, Volovich (b0010) 2003; 52 Iriyama, Ohya (b0055) 2008; 15 Iriyama, Ohya, Volovich (b0070) 2006; vol. 19 Ohya, Volovich (b0050) 2011 10.1016/j.amc.2011.05.024_b0045 Iriyama (10.1016/j.amc.2011.05.024_b0055) 2008; 15 10.1016/j.amc.2011.05.024_b0095 Deutsch (10.1016/j.amc.2011.05.024_b0020) 1985; 400 10.1016/j.amc.2011.05.024_b0085 Ohya (10.1016/j.amc.2011.05.024_b0010) 2003; 52 Asano (10.1016/j.amc.2011.05.024_b0105) 2010 10.1016/j.amc.2011.05.024_b0025 Accardi (10.1016/j.amc.2011.05.024_b0035) 1999; 39 Khrennikov (10.1016/j.amc.2011.05.024_b0100) 2010 Iriyama (10.1016/j.amc.2011.05.024_b0065) 2008; 15 Ohya (10.1016/j.amc.2011.05.024_b0005) 2003; 5 Iriyama (10.1016/j.amc.2011.05.024_b0070) 2006; vol. 19 Iriyama (10.1016/j.amc.2011.05.024_b0075) 2009; II Ohya (10.1016/j.amc.2011.05.024_b0015) 2000; 7 10.1016/j.amc.2011.05.024_b0080 10.1016/j.amc.2011.05.024_b0090 Ohya (10.1016/j.amc.2011.05.024_b0050) 2011 Ohya (10.1016/j.amc.2011.05.024_b0030) 1998; 37 Accardi (10.1016/j.amc.2011.05.024_b0040) 2004; 11 Iriyama (10.1016/j.amc.2011.05.024_b0060) 2008; 372 |
| References_xml | – reference: S. Iriyama, M. Ohya, Quantum Algorithm for Pebble Game and Its Computational Complexity, TUS preprint, 2010. – reference: S. Iriyama, M. Ohya, I. Yamato, Quantum Algorithm of Protain Folding, TUS preprint, 2010. – volume: 372 start-page: 5120 year: 2008 end-page: 5122 ident: b0060 article-title: Note on a universal quantum turing machine publication-title: Phys. Lett. A – reference: S. Iriyama, M. Ohya, The problem to construct Unitary Quantum Turing Machine computing partial recursive functions, TUS preprint, 2009. – volume: vol. 19 start-page: 204 year: 2006 end-page: 225 ident: b0070 article-title: Generalized quantum turing machine and its application to the SAT chaos algorithm publication-title: QP-PQ: Quantum Prob. White Noise Anal – reference: S. Iriyama, M. Ohya, K. Sato, I.V. 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| SubjectTerms | Algorithms Chaos theory Complexity Computation Computational complexity Dissipation Dynamics Mathematical models Quantum algorithm Quantum Turing machine Turing machines |
| Title | Computational complexity and applications of quantum algorithm |
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