Existence of the Exact CNOT on a Quantum Computer with the Exchange Interaction |
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| Authors: | Y. Kawano K. Kimura H. Sekigawa M. Noro K. Shirayanagi M. Kitagawa M. Ozawa |
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| Affiliation: | (1) NTT Communication Science Laboratories, NTT Corporation, 3-1, Morinosato Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan;(2) Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan;(3) Department of Mathematics, Kobe University, Nada-ku, Kobe 657-8501, Japan;(4) Graduate School of Engineering Science, Osaka University, Toyonaka-shi, Osaka 560-8531, Japan;(5) NTT Communication Science Laboratories, NTT Corporation, 3-1, Morinosato Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan;(6) Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan;(7) Japan Science and Technology Agency, Japan |
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| Abstract: | We prove the existence of the exact CNOT gate on aquantum computer with the nearest-neighbor exchange interaction in the serial operation mode. Its existence has been an open problem, though a concrete sequence of exchange operations, which is approximately locally equivalent to the exact CNOT, has already been found. We found the exact values of time parameters (exchange rates between qubits) by using computer algebraic techniques such as Gröbner bases and resultants. These techniques have been widely used for finding rigorous solutions of simultaneous algebraic equations, and here are applied to finding quantum gates on the decoherence-free subsystem for the first time.PACS: 02.70.Wz, 03.65.Yz, 03.67.Lx |
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| Keywords: | Quantum computation decoherence-free subsystem computer algebra Grö bner basis resultant |
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