The effect of electron-nuclear spin interactions on qubit operations is investigated for a qubit represented by the spin of an electron localized in an InGaAs self-assembled quantum dot. The localized electron wave function is evaluated within the atomistic tight-binding model. The electron Zeeman splitting induced by the electron-nuclear spin interaction is estimated in the presence of an inhomogeneous environment characterized by a random nuclear spin configuration, by the dot-size distribution, alloy disorder, and interface disorder. Due to these inhomogeneities, the electron Zeeman splitting varies from one qubit to another by the order of 10−6, 10−6, 10−7, and 10−9 eV, respectively. Such fluctuations cause errors in exchange operations due to the inequality of the Zeeman splitting between two qubits. However, the error can be made lower than the quantum error threshold if an exchange energy larger than 10−4 eV is used for the operation. This result shows that the electron-nuclear spin interaction does not hinder quantum-dot based quantum computer architectures from being scalable even in the presence of inhomogeneous environments.
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