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arXiv:1102.0762 · Physical Review A

Heisenberg spin bus as a robust transmission line for quantum-state transfer

Sangchul Oh, Lian-Ao Wu, Yun-Pil Shim, Jianjia Fei, Mark G. Friesen, Xuedong Hu

Published Aug 24, 2011• 46 citations
arXivHTMLPDF

Abstract

We study quantum-state transfer (QST) through a strongly coupled antiferromagnetic spin chain (acting as a spin bus), between weakly coupled external qubits. By treating the weak coupling as a perturbation, we find that QST is enabled specifically by the second-order terms in the perturbative expansion. We show that QST is robust against disorder in the couplings, either within the bus or to the external qubits. We find that the protocol works when the qubits are attached to any node on an even-size bus or to the antiferromagnetic nodes on an odd-size bus. The optimal time for QST is found to depend nonmonotonically on qubit separation.

DOI
10.1103/physreva.84.022330

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The effective Heisenberg interaction is generated by weakly interacting qubits with two strongly coupled chains. The system of two coupled chains can be regarded as a quantum bus. Universal quantum computation is enabled by restricting the bus to its ground state. The effective interaction is primarily determined by the energy spectrum of the bus. The interactions alternate between antiferromagnetic and ferromagnetic ones. The long-range interaction can also be attained in coupled chains with infinite size. The quantum gate operations with high precision can be realized when the quantum fluctuations are taken into account.
Based on shortcuts to adiabaticity and quantum Zeno dynamics, we present a protocol to implement quantum state transfer (QST) in a quantum spin-12\frac{1}{2}21​ chain. In the protocol, the complex Hamiltonian of an NNN-site system is simplified, and a simple effective Hamiltonian is present. It is shown that only the control of the coupling strengths between the boundary spins and the bulk spins are required for QST. Numerical simulations demonstrate that the protocol possesses high efficiency and is robust against the decay and the fluctuations of the control fields. The protocol might provide an alternative choice for transferring quantum states via spin chain systems.
The transmission of quantum information between different parts of a quantum computer is of fundamental importance. Spin chains have been proposed as quantum channels for transferring information. Different configurations for the spin couplings were proposed in order to optimize the transfer. As imperfections in the creation of these specific spin-coupling distributions can never be completely avoided, it is important to find out which systems are optimally suited for information transfer by assessing their robustness against imperfections or disturbances. We analyze different spin coupling distributions of spin chain channels designed for perfect quantum state transfer. In particular, we study the transfer of an initial state from one end of the chain to the other end. We quantify the robustness of different coupling distributions against perturbations and we relate it to the properties of the energy eigenstates and eigenvalues. We find that the localization properties of the systems play an important role for robust quantum state transfer.