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arXiv:0808.2549 · Physical Review A

SWAP operation in the two-qubit HeisenbergXXZmodel: Effects of anisotropy and magnetic field

Yue Zhou, Guofeng Zhang, Fuhua Yang, Songlin Feng

Published Jun 6, 2007• 13 citations
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Abstract

In this paper we study the SWAP operation in a two-qubit anisotropic $XXZ$ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter $\ensuremath{\lambda}$ within which the SWAP operation is feasible. The SWAP errors caused by the inhomogeneous field are evaluated.

DOI
10.1103/physreva.75.062304

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In this paper we study the SWAP operation in a two-qubit anisotropic XXZXXZXXZ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter \ensuremathλ\ensuremath{\lambda}\ensuremathλ within which the SWAP operation is feasible. The SWAP errors caused by the inhomogeneous field are evaluated.
Spin model plays an important role in the realization of quantum information processing. Quantum entanglement can be constructed, also （swap）n quantum logic gate is available if anisotropy is ignored, when Heisenberg interaction between spins is used; thus a complete quantum computing gate will be realized by combining single-qubit rotation gate. To study the influence of anisotropy on logic gate has high academic value since anisotropy is inevitable in any solid material. In this paper, swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field is discussed. The swap errors caused by the anisotropy parameter ν of the exchange interaction between spins and the inhomogeneous field δ are evaluated. We can see clearly when the swap operation can be approximately used as an ideal swap gate.
We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double-quantum-dot artificial molecule, projected to be used as a two-qubit quantum gate in the proposed quantum-dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method, which is carried out analytically, and the molecular orbital method, which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting that swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.
The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field ( B ), a parameter b which controls the inhomogeneity of B , and the bilinear interaction parameters J x = J y ≠ J z on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of J z and lower values of B and b .