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Science China Physics Mechanics and Astronomy

Controllability of spin 1 systems and realization of ternary SWAP gate in two spin 1 systems coupled with Ising interaction

Yan Wang, Yao-Min Di, Hai‐Rui Wei

Published Aug 25, 2010• 1 citation
Publisher
DOI
10.1007/s11433-010-4110-2

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We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Cartan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices. It is equivalent to exerting a certain control field on the system, and the control goal is usually gained by a sequence of control pulses. The general discussion on the realization of 2-qutrit logic gate is made first, and then the realization of the ternary SWAP gate and the ternary gate are discussed specifically, and the sequences of control pulses and drift processes implementing these gates are given.
We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Cartan decomposition of matrices,the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices.It is equivalent to exerting a certain control field on the system,and the control goal is usually gained by a sequence of control pulses.The general discussion on the realization of 2-qutrit logic gate is made first,and then the realization of the ternary SWAP gate and the ternry SWAP~(1/2)gate are discussed specifically,and the sequences of control pulses and drift processes implementing these gates are given.
In this paper, the synthesis and implementation of three-quhit SWAP gate is discussed. The three-quhit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Research illustrated that although the result is very simple, the current methods of matrix decomposition for multi-qubit gate can not get that. Then the implementation of three-qubit SWAP gate in the three spin system with Ising interaction is investigated and the sequence of control pulse and drift process to implement the gate is given. It needs 23 control pulses and 12 drift processes. Since the interaction can not be switched on and off at will, the realization of three-qubit SWAP gate in specific quantum system also can not simply come down to 2 two-qubit SWAP gates.