Existence of the Exact CNOT on a Quantum Computer with the Exchange Interaction

Authors:
Y. Kawano;K. Kimura;H. Sekigawa;M. Noro;K. Shirayanagi;M. Kitagawa;M. Ozawa
Affiliations:
NTT Communication Science Laboratories, NTT Corporation, Kanagawa, Japan 243-0198;Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;NTT Communication Science Laboratories, NTT Corporation, Kanagawa, Japan 243-0198;Department of Mathematics, Kobe University, Kobe, Japan 657-8501;NTT Communication Science Laboratories, NTT Corporation, Kanagawa, Japan 243-0198;Aff4 Aff5 Aff7;Aff6 Aff7
Venue:
Quantum Information Processing
Year:
2005

Citing 2
Cited 1

Quantum computation and quantum information

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Universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem

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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.