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

Existence of the Exact CNOT on a Quantum Computer with the Exchange Interaction 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer Science+Business Media, Inc.
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-005-4480-y
Publisher site
See Article on Publisher Site

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 8, 2005

References

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