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New quantum algorithm solving the NP complete problem. (English) Zbl 1251.81029

Summary: We review the quantum chaos algorithm solving the NP-complete problems in polynomial time. This work has been done in the series of papers with Professor Igor Volovich for nearly ten years.

MSC:

81P68 Quantum computation
81Q50 Quantum chaos
Full Text: DOI

References:

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[13] S. Iriyama and M. Ohya, ”Rigorous estimation of the computational complexity for OV SAT algorithm,” Open Syst. Inform. Dyn. 15(2), 173–187 (2008). · Zbl 1144.81442 · doi:10.1142/S1230161208000158
[14] S. Iriyama, T. Miyadera and M. Ohya, ”Note on a universal quantum Turing machine,” Phys. Lett. A 372, 5120–5122 (2008). · Zbl 1221.81042 · doi:10.1016/j.physleta.2008.05.069
[15] S. Iriyama and M. Ohya, ”Language classes defined by generalized quantum Turing machine,” Open Syst. Inform. Dyn. 15(4), 383–396 (2008). · Zbl 1188.81046 · doi:10.1142/S1230161208000262
[16] S. Iriyama, M. Ohya and I. V. Volovich, ”Generalized quantum Turing machine and its application to the SAT chaos algorithm,” QP-PQ: Quantum Prob. White Noise Anal., Quantum Inform. Comput. 19, 204–225 (World Sci. Publ., 2006).
[17] S. Iriyama, M. Ohya and I. V. Volovich, ”On computational complexity of Shor’s quantum factoring algorithm,” TUS Preprint (2012). · Zbl 1325.81054
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[19] S. Iriyama, M. Ohya and I. V. Volovich, ”On quantum algorithm for binary search and its computational complexity,” TUS Preprint (2012). · Zbl 1328.81080
[20] Goto, S. Iriyama, M. Ohya and I. V. Volovich, ”New proof of the factoring algorithm,” in preparation. · Zbl 1325.81054
[21] S. Iriyama and M. Ohya, ”The problem to construct unitary quantum Turing machine computing partial recursive functions,” TUS Preprint (2009). · Zbl 1188.81045
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